Logic Seminar 17 Aug 2022 17:00 hrs at NUS by Wong Tin Lok
NUS Logic Seminar
8/12/2022 2:30:59
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 17 August 2022, 17:00 hrs
Location: S17#04-05, Department of Mathematics, NUS
Speaker: Wong Tin Lok
Title: Another quantifier-elimination result in arithmetic
under negated induction
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract: I will present another quantifier-elimination result in arithmetic
under negated induction. This gives new information about pigeonhole
principles and expansions to second-order models.
Joint work with: David Belanger, CT Chong, Wei Li and Yue Yang
Logic Seminar Wednesday 10 Aug 2022 17:00 hrs at NUS, Room S17#04-05
NUS Logic Seminar
8/7/2022 22:09:42
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 10 August 2022, 17:00 hrs
Talk in person: Department of Mathematics, Room S17#04-05
Speaker: Tran Chieu-Minh
Title: O-minimal Methods and Generalized Sum-Product Phenomena
For a bivariate P(x,y) in R[x,y] - (R[x] union R[y]),
we show that for all finite subsets A of R,
|P(A,A)| is greater or equal alpha |A|^(5/4)
with alpha = alpha(deg P) being a real number greater than 0,
P(x,y)=f(gamma u(x)+delta u(y)) or
P(x,y)=f(u^m(x)u^n(y)) for some univariate f, u R[t] - ,
constants gamma, delta in R - {0} and
m, n in {1,2,3,...}.
This resolves the symmetric nonexpanders classification problem
proposed by de Zeeuw and is a step towards the analog for polynomials
of the Erdoes-Szemeredi sumproduct Conjecture.
The proofs of our results use tools from semialgebraic / o-minimal
geometry.
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Wednesday seminar
Prague Set Theory Seminar
8/5/2022 11:27:12
Dear all,
The seminar meets on Wednesday August 10th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: Michael Hrusak -- TBD
updates at https://calendar.math.cas.cz/seminar-on-reckoning-actual
The seminar should start meeting regularly again in September.
Best,
David
Barcelona Set Theory Seminar
Barcelona Logic Seminar
7/15/2022 3:29:13
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: Omer Ben-Neria
TITLE: Diamond, Compactness, and product approximations
ABSTRACT: It is well known that certain compactness principles imply the existence of diamonds. A long-standing open problem in the area asks if a weakly compact cardinal must carry a diamond sequence. We introduce a weak form of the diamond
principle given in terms of function estimates on products of cardinals. We use the weaker principle to find new methods for forcing the failure of diamonds at inaccessible, Mahlo, and stationary reflecting cardinals and show that the weaker principle must
hold at a weakly compact cardinal. This is joint work with Jing Zhang.
DATE: Wednesday, 20 July 2022
TIME: 16:00 (CEST)
PLACE: The Seminar will take place in person at IMUB, and online via Zoom:
Meeting ID: 985 6524 7347
Passcode: 243408
Best regards,
Joan
P.S.: If you do not wish to receive any more announcements, please send an email to
bagaria@ub.edu with the text “Unsubscribe”.
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
joan.bagaria@icrea.cat
bagaria@ub.edu
RIMS Set Theory Workshop: October 25-28, 2022
Conference
7/14/2022
Let me announce RIMS Set Theory Workshop 2022. This year’s workshop will be a hybrid one at RIMS, Kyoto University, Japan and online via Zoom.
RIMS Set Theory Workshop 2022
- New Developments in Forcing and Cardinal Arithemtic -
dates: October 25th — 28th, 2022
venue: RIMS, Kyoto University, Japan & Online via Zoom
organizer: Hiroshi Sakai (Kobe)
web page: https://sites.google.com/view/rimssettheory2022/home
We plan the following mini-course and invited talks:
Mini-Course:
- Itay Neeman (UCLA)
Invited Talks:
- David Aspero (East Anglia)
- Teruyuki Yorioka (Shizuoka)
- Rahman Mohammadpour (TU Vienna)
We also encourage you to contribute with talks. Of course, we welcome participations without talks. Abstract submission and registration can be done at the web page of the workshop. Dead lines are as follows:
Abstract Submission: until September 10th
Registration: until October 15th
Please feel free to contact the organizer (hrshsakai@gmail.com) if you have any questions.
We are looking forward to your participation!
Tagged: Itay Neeman, David Aspero, Teruyuki Yorioka, Rahman Mohammadpour
Wednesday seminar
Prague Set Theory Seminar
6/26/2022 16:18:33
Dear all,
The seminar meets on Wednesday June 29th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
The seminar will not meet during July. The seminar might meet next time
on Wednesday August 10th for a talk of Michael Hrusak.
Regular seminars should start again in September.
Program (June 29): Michal Doucha -- Generic actions of groups on the
Cantor space (continued)
In the second part of the talk I will continue with an introduction to
the symbolic dynamics. I will introduce notions such as shifts of finite
type, sofic shifts, and I will mention the Curtis-Hedlund-Lyndon theorem
which describes continuous equivariant maps between shifts. Then with
this knowledge, I will show how certain inverse limits of shifts of
finite type (or of sofic shifts) define generic actions on the Cantor
space. I won't expect the audience to remember too much from the first talk.
Best,
David
(KGRC) seminar talks Tuesday, June 28 and Thursday, June 30
Kurt Godel Research Center
6/24/2022 9:16:02
The KGRC welcomes as guests:
David Schrittesser (host: Vera Fischer) visits the KGRC until August 31.
Alessandro Vignati (host: Vera Fischer) visits the KGRC from June 30 to
July 1 and gives a talk on June 30, see below.
Severin Mejak (hosts: Vera Fischer, David Schrittesser) visits the KGRC
from July 5 to July 14.
Justin Moore (host: Vera Fischer) visits the KGRC from July 15 to July 23.
Jeffrey Bergfalk (host: Vera Fischer) visits the KGRC from July 16 to July
23.
Leandro Aurichi (host: Lyubomyr Zdomskyy) visits the KGRC from July 18 to
August 6.
Frank Tall (host: Lyubomyr Zdomskyy) visits the KGRC from July 18 to July
22.
Peter Nyikos (host: Lyubomyr Zdomskyy) visits the KGRC from July 18 to
July 22.
* * *
Set Theory Research Seminar
Kurt Gödel Research Center
Tuesday, June 28
Doctoral and master students specialising in set theory will speak on
selected topics from their work during the semester. Detailed program with
titles and abstracts is in the attachment.
Time and Place
Talk at 3:00pm in hybrid mode, in person as well as via Zoom.
Universität Wien
Institut für Mathematik
Kolingasse 14-16
1090 Wien
3:00pm - 4:30pm (Fortunato, Lukas and Alexander):
1st floor
Seminar room 10
4:45pm - 6:15pm (Ömer, Julia and Roman):
2nd floor
Seminar room 17
Zoom: If you need the Zoom data and have not received the meeting link by
the day before the talks, please contact richard.springer@univie.ac.at!
(Please direct any other requests about the Set Theory Seminar and its
Zoom meeting to vera.fischer@univie.ac.at.)
Students at Uni Wien are strongly encouraged to attend the seminar in person.
* * *
Logic Colloquium
Kurt Gödel Research Center
Thursday, June 30
"Set theory and coronas of C*-algebras"
Alessandro Vignati
(Université de Paris, FR)
As abelian C*-algebras correspond functorially to locally compact Hausdorff
space, studying C*-algebras is often viewed as noncommutative topology. A
locally compact Hausdorff space X can be embedded densely in its Čech-Stone
compactification beta X, the `largest compact space in which X sits densely'.
Similarly, to every nonunital C*-algebras A one can associate `the largest
unital C*-algebra in which A sit densely', the multiplier algebra M(A). Corona
C*-algebras, quotients of the form M(A)/A, correspond to Čech-Stone remainders
(space of the form beta X minus X).
Čech-Stone remainders have been studied with set theoretical methods since the
'80s. The work of Rudin, Shelah, Steprans, Velickovic, and Farah among others,
showed that the structure of the space beta X minus X, and its
autohomeomorphisms, often depend on the set theoretic axioms in play. Similar
phenomenons appear when studying corona C*-algebras, as Farah's work on the
Calkin algebra (the corona algebra of the compact operators) witnesses. This
talk is dedicated to overview how different axioms in set theory impact the
structure of automorphisms of corona C*-algebras.
Time and Place
Talk at 3:00pm in hybrid mode, in person as well as via Zoom
Universität Wien
Institut für Mathematik
Lecture Hall HS 13
2nd floor
Oskar-Morgenstern-Platz 1
1090 Wien
Zoom: If you need the Zoom data and have not received the meeting link by
the day before the talk, please contact richard.springer@univie.ac.at!
Tagged: Fortunato Maesano, Lukas Schembecker, Marlene Koelbing, Alexander Wendlinger, Ömer Faruk Bag, Julia Millhouse, Roman Doerner
Barcelona Set Theory Seminar
Barcelona Logic Seminar
6/19/2022 5:33:44
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: Jeffrey Bergfalk
TITLE: Higher derived limits and higher dimensional partitions of partial orders
DATE: 22 June 2022
TIME: 16:00 (CEST)
PLACE: The Seminar will take place online via Zoom:
Meeting ID: 985 6524 7347
Passcode: 243408
Best regards,
Joan
P.S.: If you do not wish to receive any more announcements, please send an email to
bagaria@ub.edu with the text “Unsubscribe”.
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
joan.bagaria@icrea.cat
bagaria@ub.edu
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
joan.bagaria@icrea.cat
bagaria@ub.edu
(KGRC) Set Theory Seminar Tuesday, June 21
Kurt Godel Research Center
6/17/2022 4:11:38
David Schrittesser (host: Vera Fischer) visits the KGRC until August 31 and
gives a talk on June 21, see below.
Gunter Fuchs (host: Vera Fischer) visits the KGRC from June 12 to June 18.
Alessandro Vignati (host: Vera Fischer) visits the KGRC from June 30 to July 1
and gives a talk on June 30. Details for this talk will be announced later.
Justin Moore (host: Vera Fischer) visits the KGRC from July 15 to July 23.
Leandro Aurichi (host: Lyubomyr Zdomskyy) visits the KGRC from July 18 to
August 6.
Frank Tall (host: Lyubomyr Zdomskyy) visits the KGRC from July 18 to July 22.
Peter Nyikos (host: Lyubomyr Zdomskyy) visits the KGRC from July 18 to July 22.
* * *
Set Theory Research Seminar
Kurt Gödel Research Center
Tuesday, June 21
"The Ramsey property, MAD families, and their higher dimensional relatives"
David Schrittesser (University of Toronto, Canada)
Infinite maximal almost disjoint families, dubbed "MAD families" by A.R.D.
Mathias, have long been an object of interest in set theory, topology, and
other areas. A question which has been tossed around for quite a while was
whether there can exist an analytic Fin^2-MAD family - that is, a
two-dimensional variant of the usual notion of MAD family. Analytic
(one-dimensional) MAD families cannot exist, so the conjecture has always been
"no" - and indeed the answer is "no", as was shown in joint work with Törnquist
and Bakke Haga in 2016.
In 1969, Mathias asked whether Ramsey regularity rules out the existence of
(one dimensional) MAD families. This question was answered positively in joint
work with Törnquist in 2019.
But now that we know that Fin^2 MAD families behave like MAD families in some
respects, and that Ramsey regularity rules out (one dimensional) MAD families,
does Ramsey regularity also rule out the two dimensional variant?
Yes, Ramsey regularity rules out the existence of Fin^2 MAD families (also
joint work with Asger Törnquist). The result even holds for J-MAD families,
where J is an ideal in the smallest class containing the ideal of finite sets
and closed under Fubini products. I will also report on work in progress with
our student Severin Mejak.
Time and Place
Talk at 3:00pm in hybrid mode, in person as well as via Zoom.
Universität Wien
Institut für Mathematik
Kolingasse 14-16
1090 Wien
1st floor
Seminar room 10
Zoom: If you need the Zoom data and have not received the meeting link by
the day before the talk, please contact richard.springer@univie.ac.at!
(Please direct any other requests about the Set Theory Seminar and its
Zoom meeting to vera.fischer@univie.ac.at.)
Students at Uni Wien are strongly encouraged to attend the seminar in person.
Wednesday seminar
Prague Set Theory Seminar
6/16/2022 4:16:34
Dear all,
The seminar meets on Wednesday June 22nd at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: Michal Doucha -- Generic actions of groups on the Cantor space
In 2004, Kechris and Rosendal proved that there is a generic
homeomorphism of the Cantor space. In other words, there is a generic
action of the group of the integers on the Cantor space. Few years
later, this was proved to be false when Z is replaced by Z^d, d>1, by
Hochman, resp. to be still valid when Z is replaced by a general
finitely generated free group, by Kwiatkowska. I found a
characterization of countable groups admitting generic actions in terms
of subshifts of finite type over such groups that allows to produce more
examples and non-examples.
I plan a gentle talk where I will not bother the audience with general
groups (unless I am asked to do so) and just try to explain some ideas
on the example of the integers. In particular, I will give an
introduction to symbolic dynamics and shifts of finite type and say how
with these objects we can construct the generic homeomorphism of the
Cantor space.
Best,
David
Wednesday seminar
Prague Set Theory Seminar
6/13/2022 5:23:38
Dear all,
The seminar meets on Wednesday June 15th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
The program is not yet decided, walk-in speakers will be welcome.
Best,
David
Krzysztof Zakrzewski, Elementary submodels and Corson-compact spaces
IMPAN Working Group in Applications of Set Theory
6/11/2022 4:59:33
Seminar: Working group in applications of set theory, IMPAN
Tuesday, 14.06.2022, at 13.15, room 403
Speaker: Krzysztof Zakrzewski (MIM UW)
Title: Elementary submodels and Corson-compact spaces.
Abstact: "We will present a characterisation of Corson-compact spaces using elementary submodels and use it to show a theorem proved earlier by Gul'ko stating that a Hausdorff continuous image of a Corson-compact space is Corson-compact."
This seems to be the last talk of this semester.
https://www.impan.pl/~set_theory/Seminar/
Barcelona Set Theory Seminar
Barcelona Logic Seminar
6/10/2022 3:14:59
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: Kameryn William
TITLE: Inner mantles: the good, bad, and ugly
DATE: 15 June 2022
TIME: 16:00 (CEST)
PLACE: The Seminar will take place online via Zoom:
Meeting ID: 985 6524 7347
Passcode: 243408
Best regards,
Joan
P.S.: If you do not wish to receive any more announcements, please send an email to
bagaria@ub.edu with the text “Unsubscribe”.
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
joan.bagaria@icrea.catbagaria@ub.edu
Cross-Alps Logic Seminar (speaker: Sonia L'Innocente)
Cross-Alps Logic Seminar
6/7/2022 8:43:42
On Friday 10.06.2022 at 16:00
Sonia L'Innocente (University of Camerino)
will give a talk on
A factorisation theory for generalised power series
Please refer to the usual webpage of our
LogicGroup
for more details and the abstract of the talk.
The seminar will be held remotely through Webex. Please write to
luca.mottoros [at] unito [dot] itfor the link to the event.
The Cross-Alps Logic Seminar is co-organized by the logic groups of
Genoa, Lausanne, Turin and Udine as part of our collaboration in the
project PRIN 2017 'Mathematical logic: models, sets, computability'.
Barcelona Set Theory Seminar
Barcelona Logic Seminar
6/3/2022 3:01:41
Dear All,
on Wednesday, the seminar will take place in hybrid from at the IMUB.
Hope to see you there!
Best,
Joan
Inici del missatge reenviat:
Tema: Barcelona Set Theory Seminar
Data: 3 de juny de 2022, 8:56:35 CEST
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: William Mance
TITLE: Descriptive complexity in number theory and dynamics
DATE: 8 June 2022
TIME: 16:00 (CEST)
PLACE: The Seminar will take place online via Zoom:
Meeting ID: 985 6524 7347
Passcode: 243408
Best regards,
Joan
P.S.: If you do not wish to receive any more announcements, please send an email to
bagaria@ub.edu with the text “Unsubscribe”.
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
joan.bagaria@icrea.catbagaria@ub.edu
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
joan.bagaria@icrea.catbagaria@ub.edu
Barcelona Set Theory Seminar
Barcelona Logic Seminar
6/3/2022 2:56:36
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: William Mance
TITLE: Descriptive complexity in number theory and dynamics
DATE: 8 June 2022
TIME: 16:00 (CEST)
PLACE: The Seminar will take place online via Zoom:
Meeting ID: 985 6524 7347
Passcode: 243408
Best regards,
Joan
P.S.: If you do not wish to receive any more announcements, please send an email to
bagaria@ub.edu with the text “Unsubscribe”.
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
joan.bagaria@icrea.catbagaria@ub.edu
Wednesday seminar
Prague Set Theory Seminar
6/2/2022 5:20:34
Dear all,
There will be no seminar next week, Wednesday June 8th (many regular
seminar participants are away).
It is unclear whether the seminar will regularly meet in June and during
the summer. No announcement = no seminar.
Best,
David
This Week in Logic at CUNY
This Week in Logic at CUNY
5/29/2022 22:30:00
Hi everyone,
This will be our final mailing of "This Week in Logic" for the Spring 2022 semester. We will resume regular mailings at the end of August (but will also send out special announcements for any summer talks).
May your time between semesters be fruitful,
Jonas
This Week in Logic at CUNY:
- - - - Monday, May 30, 2022 - - - -
- - - - Tuesday, May 31, 2022 - - - -
Models of Peano Arithmetic (MOPA)
Tuesday, May 31, 8pm
Virtual (email Victoria Gitman
vgitman@nylogic.org for meeting id)
Tin Lok Wong, National University of Singapore
Another quantifier-elimination result in arithmetic under negated induction
In a paper published in 1990, Kossak showed that all countable models of Σn collection where Σn induction fails have continuum-many automorphisms. We extract from his proof a(nother) quantifier-elimination result. This gives new information about pigeonhole principles and expansions to second-order models. The work is joint with David Belanger, CT Chong, Wei Li, and Yue Yang at the National University of Singapore.
- - - - Wednesday, Jun 1, 2022 - - - -
- - - - Thursday, Jun 2, 2022 - - - -
- - - - Friday, Jun 3, 2022 - - - -
Next Week in Logic at CUNY:
- - - - Monday, Jun 6, 2022 - - - -
- - - - Tuesday, Jun 7, 2022 - - - -
- - - - Wednesday, Jun 8, 2022 - - - -
- - - - Thursday, Jun 9, 2022 - - - -
- - - - Friday, Jun 10, 2022 - - - -
- - - - Other Logic News - - - -
CONFERENCE ANNOUNCEMENT:
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to
jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email
jreitz@nylogic.org.
Jakub Andruszkiewicz, Countable support iterations of proper forcing notions
IMPAN Working Group in Applications of Set Theory
5/29/2022 14:34:46
Seminar: Working group in applications of set theory, IMPAN
Tuesday, 31.05.2022, at 13.15, room 403
Speaker: Jakub Andruszkiewicz (UW/IM PAN)
Title: Countable support iterations of proper forcing notions.
Abstact: "We present a classical result concerning iterations of proper forcings, namely that the properness is preserved by countable support iterations. We will follow section 3 of "Tools for your forcing construction" by M. Goldstern."
This seems to be the last talk of this semester.
Barcelona Set Theory Seminar
Barcelona Logic Seminar
5/28/2022 12:03:39
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: William Chan
TITLE: Almost Disjoint Families under Determinacy
DATE: 1 June 2022
TIME: 16:00 (CEST)
PLACE: The Seminar will take place online via Zoom:
Meeting ID: 985 6524 7347
Passcode: 243408
Best regards,
Joan
P.S.: If you do not wish to receive any more announcements, please send an email to
bagaria@ub.edu with the text “Unsubscribe”.
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
joan.bagaria@icrea.catbagaria@ub.edu
Wednesday seminar
Prague Set Theory Seminar
5/27/2022 4:20:38
Dear all,
The seminar meets on Wednesday June 1st at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: Jindřich Zapletal -- Noetherian graphs
I define the class of Noetherian graphs. These are the graphs in which
the canonical graph topology is Noetherian; there is also an equivalent
combinatorial definition. I show that closed Noetherian graphs without
infinite cliques have countable chromatic number and are easier to color
than most. There are many examples.
Best,
David
Cross-Alps Logic Seminar (speaker: Takako Nemoto)
Cross-Alps Logic Seminar
5/25/2022 17:33:56
On Friday 27.05.2022 at 16:00
Takako Nemoto (Japan Advanced Institute of Science and
Technology)
will give a talk on
Determinacy of infinite games and reverse mathematics
Please refer to the usual webpage of our
LogicGroup
for more details and the abstract of the talk.
The seminar will be held remotely through Webex. Please write to
luca.mottoros [at] unito [dot] itfor the link to the event.
The Cross-Alps Logic Seminar is co-organized by the logic groups of
Genoa, Lausanne, Turin and Udine as part of our collaboration in the
project PRIN 2017 'Mathematical logic: models, sets, computability'.
(KGRC) (update: Zoom) Logic Colloquium talk Thursday, June 2
Kurt Godel Research Center
5/25/2022 4:35:20
The KGRC welcomes as guests:
David Schrittesser (host: Vera Fischer) visits the KGRC until August 31 and
gives a talk on June 21. Details for this talk will be announced later.
Marta Maloid-Glebova (host: Lyubomyr Zdomskyy) visits the KGRC until May 31.
James Mitchell (host: Vera Fischer) visits the KGRC until May 28.
Yann Peresse (host: Serhii Bardyla) visits the KGRC until May 28.
Luke Elliott (host: Lyubomyr Zdomskyy) visits the KGRC until May 28.
Gunter Fuchs (host: Vera Fischer) visits the KGRC from June 12 to June 18 and
gives a talk on June 14. Details for this talk will be announced later.
Alessandro Vignati (host: Vera Fischer) visits the KGRC from June 30 to July 1
and gives a talk on June 30. Details for this talk will be announced later.
Leandro Aurichi (host: Lyubomyr Zdomskyy) visits the KGRC from July 18 to
August 6.
Peter Nyikos (host: Lyubomyr Zdomskyy) visits the KGRC from July 18 to July 22.
Frank Tall (host: Lyubomyr Zdomskyy) visits the KGRC from July 18 to July 22.
* * *
Please note that there will be no talk in the Set Theory Research Seminar on
Tuesday, May 31.
* * *
Logic Colloquium
Kurt Gödel Research Center
Thursday, June 2
"The metamathematics of $\Pi^1_2$ sentences"
Juan Aguilera (TU Wien)
We will survey some recent results on the metamathematics of $\Pi^1_2$
sentences. Most of the work involves a kind of Proof Theory analogous to
classical ordinal analysis, but focused on a $\Pi^1_2$ notion instead. The talk
will be aimed at a general logic audience. Topics will include: proof-theoretic
$\Pi^1_2$-norms, a characterization of the $\Pi^1_2$ consequences of
arithmetical comprehension and related systems, $\Pi^1_2$-soundness ordinals,
and the $\Pi^1_2$-Spectrum Conjecture. This is joint work with F. Pakhomov.
Time and Place
Talk at 3:00pm in hybrid mode, in person as well as via Zoom:
Universität Wien
Institut für Mathematik
Lecture Hall HS 13
2nd floor
Oskar-Morgenstern-Platz 1
1090 Wien
Zoom: If you need the Zoom data and have not received the meeting link by
the day before the talk, please contact richard.springer@univie.ac.at!
This Week in Logic at CUNY
This Week in Logic at CUNY
5/22/2022 22:30:00
This Week in Logic at CUNY:
- - - - Monday, May 23, 2022 - - - -
- - - - Tuesday, May 24, 2022 - - - -
Models of Peano Arithmetic (MOPA)
Tuesday, May 24, 2pm
Virtual (email Victoria Gitman
vgitman@nylogic.org for meeting id)
Laurence Kirby, Brooklyn College
The winding road to mathematical independence results for PA
Advances in understanding the incompleteness of PA in the 1970s and 80s built on the work of an earlier generation in the 1930s and 40s. This talk will offer historical and personal reflections on what was known, and what was not known, by both generations of logicians.
- - - - Wednesday, May 25, 2022 - - - -
- - - - Thursday, May 26, 2022 - - - -
- - - - Friday, May 27, 2022 - - - -
Set Theory Seminar
CUNY Graduate Center, Friday, May 27, 12:15pm
In-person: GC Room 6496
Virtual: Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
William Chan, Carnegie Mellon University
Determinacy and Partition Properties: Part II
In this talk, we will review some basic properties of partition cardinals under the axiom of determinacy. We will be particularly interested with the strong partition property of the first uncountable cardinal and the good coding system used to derive these partition properties. We will discuss almost everywhere behavior of functions on partition spaces of cardinals with respect to the partition measures including various almost everywhere continuity and monotonicity properties. These continuity results will be used to distinguish some cardinalities below the power set of partition cardinals. We will also use these continuity results to produce upper bounds on the ultrapower of the first uncountable cardinal by each of its partition measures, which addresses a question of Goldberg. Portions of the talk are joint work with Jackson and Trang.
Next Week in Logic at CUNY:
- - - - Monday, May 30, 2022 - - - -
- - - - Tuesday, May 31, 2022 - - - -
Models of Peano Arithmetic (MOPA)
Tuesday, May 31, 8pm
Virtual (email Victoria Gitman
vgitman@nylogic.org for meeting id)
Tin Lok Wong National University of Singapore
- - - - Wednesday, Jun 1, 2022 - - - -
- - - - Thursday, Jun 2, 2022 - - - -
- - - - Friday, Jun 3, 2022 - - - -
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
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jreitz@nylogic.org.
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jreitz@nylogic.org.
Wednesday seminar
Prague Set Theory Seminar
5/21/2022 9:16:35
Dear all,
The seminar meets on Wednesday May 25th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: Tommaso Russo -- Walks on ordinals and scattered compact spaces
I will present a construction of a scattered compact topological space
that answered a question due to Wiesław Kubiś and Arkady Leiderman. The
construction is contained in a joint paper with Petr Hájek, Jacopo
Somaglia, and Stevo Todorčević. The purpose of the paper was actually to
answer a problem in Banach space theory, but for the sake of the talk I
will focus on the construction of the compact space and not mention
Banach spaces at all. In the talk I will give a short introduction to
Descriptive Topology in order to explain the setting and to motivate the
construction of the example. Then I will explain how to use the
combinatorics of the set of countable ordinals, in particular
Todorčević's theory of walks on ordinals, for the construction of the
example.
P.Hájek, T.Russo, J.Somaglia, and S.Todorčević,
An Asplund space with norming Markuševič basis that is not weakly
compactly generated,
https://doi.org/10.1016/j.aim.2021.108041
Adv. Math. 392 (2021), 108041.
Best,
David
Barcelona Set Theory Seminar
Barcelona Logic Seminar
5/20/2022 15:40:22
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: Peter Holy
TITLE: Asymmetric Cut and Choose Games
DATE: 25 May 2022
TIME: 16:00 (CEST)
PLACE: The Seminar will take place online via Zoom:
Meeting ID: 985 6524 7347
Passcode: 243408
Best regards,
Joan
P.S.: If you do not wish to receive any more announcements, please send an email to
bagaria@ub.edu with the text “Unsubscribe”.
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
joan.bagaria@icrea.catbagaria@ub.edu
(KGRC) Set Theory Research Seminar talks Tuesday, May 24 and WEDNESDAY, May 25
Kurt Godel Research Center
5/19/2022 4:06:24
The KGRC welcomes as guests:
David Schrittesser (host: Vera Fischer) visits the KGRC until August 31
and gives a talk on June 21. Details for this talk will be announced
later.
Marta Maloid-Glebova (host: Lyubomyr Zdomskyy) visits the KGRC until May
31.
Jonathan Cancino (host: Vera Fischer) visits the KGRC until May 20.
James Mitchell (host: Vera Fischer) visits the KGRC from May 21 to May 28
and gives a talk on May 25 (see below).
Yann Peresse (host: Serhii Bardyla) visits the KGRC from May 21 to May 28.
Luke Elliott (host: Lyubomyr Zdomskyy) visits the KGRC from May 21 to May
28 and gives a talk on May 25, see below.
Gunter Fuchs (host: Vera Fischer) visits the KGRC from June 12 to June 18
and gives a talk on June 14. Details for this talk will be announced
later.
Alessandro Vignati (host: Vera Fischer) visits the KGRC from June 30 to
July 1 and gives a talk on June 30. Details for this talk will be
announced later.
* * *
Set Theory Research Seminar
Kurt Gödel Research Center
Tuesday, May 24
"Inner Models, Determinacy, and Sealing"
Sandra Müller
(TU Wien)
Inner model theory has been very successful in connecting determinacy
axioms to the existence of inner models with large cardinals and other
natural hypotheses. Recent results of Larson, Sargsyan, and Trang suggest
that a Woodin limit of Woodin cardinals is a natural barrier for our
current methods to prove these connections. One reason for this comes from
Sealing, a generic absoluteness principle for the theory of the
universally Baire sets of reals introduced by Woodin. Woodin showed in his
famous Sealing Theorem that in the presence of a proper class of Woodin
cardinals Sealing holds after collapsing a supercompact cardinal. I will
outline the importance of Sealing and discuss a new and
stationary-tower-free proof of Woodin's Sealing Theorem that is based on
Sargsyan's and Trang's proof of Sealing from iterability. This is joint
work with Grigor Sargsyan and Bartosz Wcisło.
Time and Place
Talk at 3:00pm in hybrid mode, in person as well as via Zoom.
Universität Wien
Institut für Mathematik
Kolingasse 14-16
1090 Wien
1st floor
Seminar room 10
Zoom: If you need the Zoom data and have not received the meeting link by
the day before the talk, please contact richard.springer@univie.ac.at!
(Please direct any other requests about the Set Theory Seminar and its
Zoom meeting to vera.fischer@univie.ac.at.)
Students at Uni Wien are strongly encouraged to attend the seminar in person.
* * *
Set Theory Research Seminar
Kurt Gödel Research Center
WEDNESDAY, May 25
(Please note the unusual day and time!)
"Unindexed subshifts of finite type and a connecton to Thompsons groups"
Luke Elliott
(U of St Andrews, Scotland, UK)
I will give a brief introduction to subshifts of finite type defined by
finite directed graphs. In particular I will mention a category of
"digaphs and foldings" introduced by Jim Belk, Collin Bleak, and Peter
Cameron which is useful for studying these systems. I will then discuss my
recent work in building an analogous category in which isomorphisms don't
necessarily preserve indexing and path length. This category gives us both
more flexible notions of (strong) shift equivalence and a connection to
automorphisms of Thompsons groups.
Time and Place
(Please note the unusual day and time!)
Talk at 11:30am in hybrid mode, in person as well as via Zoom:
Universität Wien
Institut für Mathematik
Kolingasse 14-16
1090 Wien
1st floor
Seminar room 10
Zoom: If you need the Zoom data and have not received the meeting link by
the day before the talk, please contact richard.springer@univie.ac.at!
(Please direct any other requests about the Set Theory Seminar and its
Zoom meeting to vera.fischer@univie.ac.at.)
Students at Uni Wien are strongly encouraged to attend the seminar in person.
Cross-Alps Logic Seminar (speaker: Alberto Marcone)
Cross-Alps Logic Seminar
5/17/2022 2:07:07
On Friday 20.05.2022 at 16:00
Alberto Marcone (University of Udine)
will give a talk on
The transfinite Ramsey theorem
Please refer to the usual webpage of our
LogicGroup
for more details and the abstract of the talk.
The seminar will be held remotely through Webex. Please write to
luca.mottoros [at] unito [dot] it for the link to the event.
The Cross-Alps Logic Seminar is co-organized by the logic groups of
Genoa, Lausanne, Turin and Udine as part of our collaboration in the
project PRIN 2017 'Mathematical logic: models, sets, computability'.
This Week in Logic at CUNY
This Week in Logic at CUNY
5/15/2022 22:30:00
This Week in Logic at CUNY:
- - - - Monday, May 16, 2022 - - - -
Logic and Metaphysics Workshop
Date: Monday, May 16, 4.15-6.15 (NY time), GC 5382
For meeting information (including zoom link for those wishing to attend remotely), please sign up for our mailing list at
https://logic.commons.gc.cuny.edu/about/Mircea Dumitru (Bucharest)
Title: Modal Frame Incompleteness: An Account through Second Order Logic
Abstract: Propositional modal logic is usually viewed as a generalization and extension of propositional classical logic. The main argument of this paper is that a good case can be made that modal logic should be construed as a restricted form of second order classical logic. The paper makes use of the embedding of modal logic in second order logic and henceforth it goes on examining one aspect of this second order connection having to do with an incompleteness phenomenon. The leading concept is that modal incompleteness is to be explained as a kind of exemplification of standard order incompleteness. Moreover the modal incompleteness phenomenon is essentially rooted in the weaker expressive power of the language of sentential modal logic as compared to the stronger expressive power of the language of second order logic.
- - - - Tuesday, May 17, 2022 - - - -
Models of Peano Arithmetic (MOPA)
Tuesday, May 17, 2pm
Virtual (email Victoria Gitman
vgitman@nylogic.org for meeting id)
Ken McAloon, Brooklyn College
E Pluribus Unum
Athena sprang forth full grown from the head of Zeus. Newton/Leibniz created Calculus. Galois created Galois Theory. Cantor created Set Theory. Boole created Boolean Algebra.
But Models of Peano Arithmetic doesn’t have a dramatic origin myth like that and took some 100 years to emerge as a discipline in itself - from Dedekind’s Second Order Axioms for Arithmetic (1863), through Frege’s Begriffsschrift (1879) and First Order Logic, through Godel’s Completeness and Incompleteness Theorems, through Skolem’s elegant construction of a non-standard model, through the War and après-guerre and on into the 1970s where the subject at last emerges as a discipline in itself. We’ll discuss the convergence of people and ideas from diverse fields like Model Theory, Set Theory, Recursion Theory, Proof Theory, Complexity Theory, … that led to the field we know and love today.
- - - - Wednesday, May 18, 2022 - - - -
- - - - Thursday, May 19, 2022 - - - -
- - - - Friday, May 20, 2022 - - - -
Set Theory Seminar
CUNY Graduate Center, Friday, May 20, 12:15pm
In-person: GC Room 6496
Virtual: Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
William Chan, Carnegie Mellon University
Determinacy and Partition Properties
In this talk, we will review some basic properties of partition cardinals under the axiom of determinacy. We will be particularly interested with the strong partition property of the first uncountable cardinal and the good coding system used to derive these partition properties. We will discuss almost everywhere behavior of functions on partition spaces of cardinals with respect to the partition measures including various almost everywhere continuity and monotonicity properties. These continuity results will be used to distinguish some cardinalities below the power set of partition cardinals. We will also use these continuity results to produce upper bounds on the ultrapower of the first uncountable cardinal by each of its partition measures, which addresses a question of Goldberg. Portions of the talk are joint work with Jackson and Trang.
Next Week in Logic at CUNY:
- - - - Monday, May 23, 2022 - - - -
- - - - Tuesday, May 24, 2022 - - - -
- - - - Wednesday, May 25, 2022 - - - -
- - - - Thursday, May 26, 2022 - - - -
- - - - Friday, May 27, 2022 - - - -
Set Theory Seminar
CUNY Graduate Center, Friday, May 27, 12:15pm
In-person: GC Room 6496
Virtual: Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
William Chan, Carnegie Mellon University
Determinacy and Partition Properties: Part II
In this talk, we will review some basic properties of partition cardinals under the axiom of determinacy. We will be particularly interested with the strong partition property of the first uncountable cardinal and the good coding system used to derive these partition properties. We will discuss almost everywhere behavior of functions on partition spaces of cardinals with respect to the partition measures including various almost everywhere continuity and monotonicity properties. These continuity results will be used to distinguish some cardinalities below the power set of partition cardinals. We will also use these continuity results to produce upper bounds on the ultrapower of the first uncountable cardinal by each of its partition measures, which addresses a question of Goldberg. Portions of the talk are joint work with Jackson and Trang.
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to
jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email
jreitz@nylogic.org.
Barcelona Set Theory Seminar
Barcelona Logic Seminar
5/15/2022 11:38:35
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: Laura Fontanella
TITLE: Representing ordinals in classical realizability
DATE: 18 May 2022
TIME: 16:00 (CEST)
PLACE: The Seminar will take place online via Zoom:
Meeting ID: 985 6524 7347
Passcode: 243408
Best regards,
Joan
P.S.: If you do not wish to receive any more announcements, please send an email to
bagaria@ub.edu with the text “Unsubscribe”.
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
joan.bagaria@icrea.catbagaria@ub.edu
Wednesday seminar
Prague Set Theory Seminar
5/13/2022 6:32:31
Dear all,
The seminar meets on Wednesday May 18th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: David Uhrik -- Hadwiger's conjecture for infinite graphs
Hadwiger's conjecture is one of the most famous unsolved problems in
finite graph theory. I will talk about the infinite version of this
conjecture and related results.
Best,
David
(KGRC) Set Theory Research Seminar talk Tuesday, May 17 and Logic Colloquium talk Thursday, May 19
Kurt Godel Research Center
5/12/2022 13:54:11
The KGRC welcomes as guests:
Marta Maloid-Glebova (host: Lyubomyr Zdomskyy) visits the KGRC until May
31.
David Schrittesser (host: Vera Fischer) visits the KGRC until August 31
and gives a talk on June 21. Details for the talk will be announced at a
later time.
Jonathan Cancino (host: Vera Fischer) visits the KGRC from May 16 to May
20.
James Mitchell (host: Vera Fischer) visits the KGRC from May 21 to May 28
and gives a talk on May 25, 11:30am (please note the unusual time!).
Details for the talk will be announced at a later time.
Yann Peresse (host: Serhii Bardyla) visits the KGRC from May 21 to May 28.
Luke Elliott (host: Lyubomyr Zdomskyy) visits the KGRC from May 21 to May
28.
Alessandro Vignati (host: Vera Fischer) visits the KGRC from June 30 to
July 1 and gives a talk on June 30. Details for the talk will be announced
at a later time.
* * *
Set Theory Research Seminar
Kurt Gödel Research Center
Tuesday, May 17
"Patterns in the large cardinal hierarchy"
Philipp Lücke (University of Bareclona)
In my talk, I will present results showing that the existence of various
well-known large cardinals can be characterized through the validity of
strong extensions of the downward Löwenheim-Skolem theorem.
These equivalences show that certain patterns recur throughout the large
cardinal hierarchy.
In particular, they show that strongly unfoldable cardinals, introduced by
Villaveces in his model-theoretic investigations of models of set theory,
relate to subtle cardinals, introduced by Kunen and Jensen in their
studies of strong diamond principles, in the same way as supercompact
cardinals relate to Vopěnka cardinals and strong cardinals relate to
Woodin cardinals.
This is joint work in progress with Joan Bagaria (Barcelona).
Time and Place
This talk will be given via Zoom. If you need the Zoom data and have not
received the meeting link by the day before the talk, please contact
richard.springer@univie.ac.at! (Please direct any other requests about the
Set Theory Seminar and its Zoom meeting to vera.fischer@univie.ac.at.)
* * *
Logic Colloquium
Kurt Gödel Research Center
Thursday, May 19
"Axiomatizing Kaufmann Models of Arithmetic in Strong Logics"
Corey Switzer (KGRC)
A {\em Kaufmann model} of $\mathsf{PA}$ is an $\omega_1$-like, recursively
saturated, rather classless model (these terms will be defined in the
talk). Such models have been an important object of study in model theory
of arithmetic and its environs since the 70's. Kaufmann models are natural
counterexamples to several theorems about countable models of
$\mathsf{PA}$ holding at the uncountable. Moreover they are a witness to
incompactness at $\omega_1$ similar to an Aronszajn tree. The proof that
Kaufmann models exist lies along a somewhat twisted road. Kaufmann showed
that there are Kaufmann models under the combinatorial principle
$\diamondsuit_{\omega_1}$ and, later, Shelah eliminated the use of
$\diamondsuit_{\omega_1}$ by appealing to a forcing absoluteness argument
involving the strong logic $L_{\omega_1, \omega}(Q)$ where $Q$ is the
quantifier ``there exists uncountably many''. It remains an extremely
interesting, if somewhat vague, question, attributed to Hodges, whether
one can build a Kaufmann model ``by hand'' in $\mathsf{ZFC}$ without
appealing to generic absoluteness.
In this talk we will report on our recent progress in this area.
Specifically we will consider the role that the strong logic $L_{\omega_1,
\omega}(Q)$ plays in Kaufmann models and show that the statement
``Kaufmann models can be axiomatized by $L_{\omega_1, \omega}(Q)$'' is
independent of $\mathsf{ZFC}$. Along the way we will discuss how Kaufmann
models are affected by forcing and in particular show that it is
independent of $\mathsf{ZFC}$ whether or not there is a Kaufmann model
which can be ``killed" by forcing without collapsing $\omega_1$.
Time and Place
Talk at 3:00pm
Universität Wien
Institut für Mathematik
Lecture Hall HS 13
2nd floor
Oskar-Morgenstern-Platz 1
1090 Wien
TOMORROW: Vladimir Tkachuk at the Toronto Set Theory Seminar
Set Theory Seminar at the Fields Institute
5/12/2022 4:08:50
Lindelöf Σ-spaces in 2022
Speaker:
Vladimir Tkachuk, Universidad Autónoma Metropolitana
Date and Time:
Friday, May 13, 2022 - 1:30pm to 3:00pm EDT (UTC -4)
Location: https://zoom.us/j/92701726800
Abstract:
This talk is a survey and an advertisement of the theory of Lindelöf
Σ-spaces. We will present ten equivalent definitions of the Lindelöf
Σ-property and a selection of results that have numerous applications in
General Topology, Topological Algebra and C_p-theory.
http://www.fields.utoronto.ca/activities/21-22/set-theory-seminar
Cross-Alps Logic Seminar (speaker: Udayan B. Darji)
Cross-Alps Logic Seminar
5/9/2022 12:50:53
On Friday 13.05.2022 at 16:00
Udayan B. Darji (University of Louisville)
will give a talk on
Descriptive complexity and local entropy
Please refer to the usual webpage of our
LogicGroup
for more details and the abstract of the talk.
The seminar will be held remotely through Webex. Please write to
luca.mottoros [at] unito [dot] itfor the link to the event.
The Cross-Alps Logic Seminar is co-organized by the logic groups of
Genoa, Lausanne, Turin and Udine as part of our collaboration in the
project PRIN 2017 'Mathematical logic: models, sets, computability'.
UPDATE: This Week in Logic at CUNY
This Week in Logic at CUNY
5/9/2022 9:59:02
Hi everyone,
Quick correction: Tuesday's Models of Peano Arithmetic (MOPA) talk will take place at 10am (not 2pm).
Sorry for the error,
Jonas
This Week in Logic at CUNY:
- - - - Monday, May 9, 2022 - - - -
Logic and Metaphysics Workshop
Date: Monday, May 9, 4.15-6.15 (NY time), GC 5382
For meeting information (including zoom link for those wishing to attend remotely), please sign up for our mailing list at
https://logic.commons.gc.cuny.edu/about/Julian Schlöder (UConn).
Title: Neo-Pragmatism about Truth
Abstract: Deflationists about truth hold that the function of the truth predicate is to enable us to make certain assertions we could not otherwise make. Pragmatists claim that the utility of negation lies in its role in registering incompatibility. The pragmatist insight about negation has been successfully incorporated into bilateral theories of content, which take the meaning of negation to be inferentially explained in terms of the speech act of rejection. One can implement the deflationist insight in the pragmatist’s theory of content by taking the meaning of the truth predicate to be explained by its inferential relation to assertion. There are two upshots. First, a new diagnosis of the Liar, Revenges and attendant paradoxes: the paradoxes require that truth rules preserve evidence, but they only preserve commitment. Second, one straightforwardly obtains axiomatisations of several supervaluational hierarchies, answering the question of how such theories are to be naturally axiomatised. This is joint work with Luca Incurvati (Amsterdam).
- - - - Tuesday, May 10, 2022 - - - -
Models of Peano Arithmetic (MOPA)
Tuesday, May 10, 10am
Virtual (email Victoria Gitman
vgitman@nylogic.org for meeting id)
Saeed Salehi, University of Tabriz
ω-Consistency: Gödel’s “much weaker” notion of soundness
As the history goes, and was confirmed recently [vP20], Gödel first proved his first incompleteness theorem [G31] for sound theories (that extend Principia Mathematica). Later he weakened the soundness condition to “ℵ0-consistency”, which later evolved to “ω-consistency”. This condition was needed for irrefutability of (what is now called) Gödelian sentences; the simple consistency of a theory suffices for the unprovability of such sentences. Gödel already notes in [G31] that a necessary and sufficient condition for the independence of Gödelian sentences of T is just a bit more than the simple consistency of T: the consistency of T with ConT, the consistency statement of T.
In this talk, we ask the following questions and attempt at answering them, at least partially.
- Why on earth Gödel [G31] had to introduce this rather strange notion?
- Does it have any applications in other areas of logic, arithmetical theories, or mathematics?
- What was Gödel’s reason that ω-consistency is “much weaker” than soundness? He does prove in [G31] that consistency is weaker (if not much weaker) than ω-consistency; but never mentions a proof or even a hint as to why soundness is (much) stronger than ω-consistency!
- Other than those historical and philosophical questions, is this a useful notion worthy of further study?
We will also review some properties of ω-consistency in the talk.References:- [G31] Kurt Gödel (1931); “On formally undecidable propositions of Principia Mathematica and related systems I”, in: S. Feferman, et al. (eds.), Kurt Gödel: Collected Works, Vol. I: Publications 1929–1936, Oxford University Press, 1986, pp. 135–152.
- [vP20] Jan von Plato (2020); Can Mathematics Be Proved Consistent? Gödel’s Shorthand Notes & Lectures on Incompleteness, Springer.
Reviewed in the zbMATH Open at https://zbmath.org/1466.03001
- - - - Wednesday, May 11, 2022 - - - -
Tutorial: Categorical Semantics of EntropyWednesday 11 May 2022, 13:00–16:30 Eastern Time, Room 5209 at the CUNY Graduate Center and via Zoom. Organized by John Terilla.
To attend, register here.- - - - Thursday, May 12, 2022 - - - -
- - - - Friday, May 13, 2022 - - - -
Set Theory Seminar
CUNY Graduate Center, Friday, May 13, 12:15pm
In-person: GC Room 6496
Virtual: Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
Andrew Brooke-Taylor University of Leeds
CONFERENCE: Categorical Semantics of Entropy
There will be a workshop on the categorical semantics of entropy at the CUNY Grad Center in Manhattan on Friday May 13th.
John Baez uc Riverside; Centre for Quantum Technologies; Topos Institute
Tai-Danae Bradley The Master's University; Sandbox AQ
Owen Lynch Utrecht University
Tom Mainiero Rutgers New High Energy Theory Center
Arthur Parzygnat Institut des Hautes Études Scientifiques
David Spivak MIT and the Topos Instiftute
Note: There is a related tutorial taking place on May 11 (see above).
Next Week in Logic at CUNY:
- - - - Monday, May 16, 2022 - - - -
Logic and Metaphysics Workshop
Date: Monday, May 16, 4.15-6.15 (NY time), GC 5382
For meeting information (including zoom link for those wishing to attend remotely), please sign up for our mailing list at
https://logic.commons.gc.cuny.edu/about/Mircea Dumitru (Bucharest)
Title: Modal Frame Incompleteness: An Account through Second Order Logic
Abstract: Propositional modal logic is usually viewed as a generalization and extension of propositional classical logic. The main argument of this paper is that a good case can be made that modal logic should be construed as a restricted form of second order classical logic. The paper makes use of the embedding of modal logic in second order logic and henceforth it goes on examining one aspect of this second order connection having to do with an incompleteness phenomenon. The leading concept is that modal incompleteness is to be explained as a kind of exemplification of standard order incompleteness. Moreover the modal incompleteness phenomenon is essentially rooted in the weaker expressive power of the language of sentential modal logic as compared to the stronger expressive power of the language of second order logic.
- - - - Tuesday, May 17, 2022 - - - -
Models of Peano Arithmetic (MOPA)
Tuesday, May 17, 2pm
Virtual (email Victoria Gitman
vgitman@nylogic.org for meeting id)
Ken McAloon, Brooklyn College
E Pluribus Unum
Athena sprang forth full grown from the head of Zeus. Newton/Leibniz created Calculus. Galois created Galois Theory. Cantor created Set Theory. Boole created Boolean Algebra.
But Models of Peano Arithmetic doesn’t have a dramatic origin myth like that and took some 100 years to emerge as a discipline in itself - from Dedekind’s Second Order Axioms for Arithmetic (1863), through Frege’s Begriffsschrift (1879) and First Order Logic, through Godel’s Completeness and Incompleteness Theorems, through Skolem’s elegant construction of a non-standard model, through the War and après-guerre and on into the 1970s where the subject at last emerges as a discipline in itself. We’ll discuss the convergence of people and ideas from diverse fields like Model Theory, Set Theory, Recursion Theory, Proof Theory, Complexity Theory, … that led to the field we know and love today.
- - - - Wednesday, May 18, 2022 - - - -
- - - - Thursday, May 19, 2022 - - - -
- - - - Friday, May 20, 2022 - - - -
Set Theory Seminar
CUNY Graduate Center, Friday, May 20, 12:15pm
In-person: GC Room 6496
Virtual: Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
William Chan, Carnegie Mellon University
Determinacy and Partition Properties
In this talk, we will review some basic properties of partition cardinals under the axiom of determinacy. We will be particularly interested with the strong partition property of the first uncountable cardinal and the good coding system used to derive these partition properties. We will discuss almost everywhere behavior of functions on partition spaces of cardinals with respect to the partition measures including various almost everywhere continuity and monotonicity properties. These continuity results will be used to distinguish some cardinalities below the power set of partition cardinals. We will also use these continuity results to produce upper bounds on the ultrapower of the first uncountable cardinal by each of its partition measures, which addresses a question of Goldberg. Portions of the talk are joint work with Jackson and Trang.
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
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jreitz@nylogic.org.
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This Week in Logic at CUNY
This Week in Logic at CUNY
5/8/2022 22:42:00
This Week in Logic at CUNY:
- - - - Monday, May 9, 2022 - - - -
Logic and Metaphysics Workshop
Date: Monday, May 9, 4.15-6.15 (NY time), GC 5382
For meeting information (including zoom link for those wishing to attend remotely), please sign up for our mailing list at
https://logic.commons.gc.cuny.edu/about/Julian Schlöder (UConn).
Title: Neo-Pragmatism about Truth
Abstract: Deflationists about truth hold that the function of the truth predicate is to enable us to make certain assertions we could not otherwise make. Pragmatists claim that the utility of negation lies in its role in registering incompatibility. The pragmatist insight about negation has been successfully incorporated into bilateral theories of content, which take the meaning of negation to be inferentially explained in terms of the speech act of rejection. One can implement the deflationist insight in the pragmatist’s theory of content by taking the meaning of the truth predicate to be explained by its inferential relation to assertion. There are two upshots. First, a new diagnosis of the Liar, Revenges and attendant paradoxes: the paradoxes require that truth rules preserve evidence, but they only preserve commitment. Second, one straightforwardly obtains axiomatisations of several supervaluational hierarchies, answering the question of how such theories are to be naturally axiomatised. This is joint work with Luca Incurvati (Amsterdam).
- - - - Tuesday, May 10, 2022 - - - -
Models of Peano Arithmetic (MOPA)
Tuesday, May 10, 2pm
Virtual (email Victoria Gitman
vgitman@nylogic.org for meeting id)
Saeed Salehi, University of Tabriz
ω-Consistency: Gödel’s “much weaker” notion of soundness
As the history goes, and was confirmed recently [vP20], Gödel first proved his first incompleteness theorem [G31] for sound theories (that extend Principia Mathematica). Later he weakened the soundness condition to “ℵ0-consistency”, which later evolved to “ω-consistency”. This condition was needed for irrefutability of (what is now called) Gödelian sentences; the simple consistency of a theory suffices for the unprovability of such sentences. Gödel already notes in [G31] that a necessary and sufficient condition for the independence of Gödelian sentences of T is just a bit more than the simple consistency of T: the consistency of T with ConT, the consistency statement of T.
In this talk, we ask the following questions and attempt at answering them, at least partially.
- Why on earth Gödel [G31] had to introduce this rather strange notion?
- Does it have any applications in other areas of logic, arithmetical theories, or mathematics?
- What was Gödel’s reason that ω-consistency is “much weaker” than soundness? He does prove in [G31] that consistency is weaker (if not much weaker) than ω-consistency; but never mentions a proof or even a hint as to why soundness is (much) stronger than ω-consistency!
- Other than those historical and philosophical questions, is this a useful notion worthy of further study?
We will also review some properties of ω-consistency in the talk.References:- [G31] Kurt Gödel (1931); “On formally undecidable propositions of Principia Mathematica and related systems I”, in: S. Feferman, et al. (eds.), Kurt Gödel: Collected Works, Vol. I: Publications 1929–1936, Oxford University Press, 1986, pp. 135–152.
- [vP20] Jan von Plato (2020); Can Mathematics Be Proved Consistent? Gödel’s Shorthand Notes & Lectures on Incompleteness, Springer.
Reviewed in the zbMATH Open at https://zbmath.org/1466.03001
- - - - Wednesday, May 11, 2022 - - - -
Tutorial: Categorical Semantics of EntropyWednesday 11 May 2022, 13:00–16:30 Eastern Time, Room 5209 at the CUNY Graduate Center and via Zoom. Organized by John Terilla.
To attend, register here.- - - - Thursday, May 12, 2022 - - - -
- - - - Friday, May 13, 2022 - - - -
Set Theory Seminar
CUNY Graduate Center, Friday, May 13, 12:15pm
In-person: GC Room 6496
Virtual: Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
Andrew Brooke-Taylor University of Leeds
CONFERENCE: Categorical Semantics of Entropy
There will be a workshop on the categorical semantics of entropy at the CUNY Grad Center in Manhattan on Friday May 13th.
John Baez uc Riverside; Centre for Quantum Technologies; Topos Institute
Tai-Danae Bradley The Master's University; Sandbox AQ
Owen Lynch Utrecht University
Tom Mainiero Rutgers New High Energy Theory Center
Arthur Parzygnat Institut des Hautes Études Scientifiques
David Spivak MIT and the Topos Instiftute
Note: There is a related tutorial taking place on May 11 (see above).
Next Week in Logic at CUNY:
- - - - Monday, May 16, 2022 - - - -
Logic and Metaphysics Workshop
Date: Monday, May 16, 4.15-6.15 (NY time), GC 5382
For meeting information (including zoom link for those wishing to attend remotely), please sign up for our mailing list at
https://logic.commons.gc.cuny.edu/about/Mircea Dumitru (Bucharest)
Title: Modal Frame Incompleteness: An Account through Second Order Logic
Abstract: Propositional modal logic is usually viewed as a generalization and extension of propositional classical logic. The main argument of this paper is that a good case can be made that modal logic should be construed as a restricted form of second order classical logic. The paper makes use of the embedding of modal logic in second order logic and henceforth it goes on examining one aspect of this second order connection having to do with an incompleteness phenomenon. The leading concept is that modal incompleteness is to be explained as a kind of exemplification of standard order incompleteness. Moreover the modal incompleteness phenomenon is essentially rooted in the weaker expressive power of the language of sentential modal logic as compared to the stronger expressive power of the language of second order logic.
- - - - Tuesday, May 17, 2022 - - - -
Models of Peano Arithmetic (MOPA)
Tuesday, May 17, 2pm
Virtual (email Victoria Gitman
vgitman@nylogic.org for meeting id)
Ken McAloon, Brooklyn College
E Pluribus Unum
Athena sprang forth full grown from the head of Zeus. Newton/Leibniz created Calculus. Galois created Galois Theory. Cantor created Set Theory. Boole created Boolean Algebra.
But Models of Peano Arithmetic doesn’t have a dramatic origin myth like that and took some 100 years to emerge as a discipline in itself - from Dedekind’s Second Order Axioms for Arithmetic (1863), through Frege’s Begriffsschrift (1879) and First Order Logic, through Godel’s Completeness and Incompleteness Theorems, through Skolem’s elegant construction of a non-standard model, through the War and après-guerre and on into the 1970s where the subject at last emerges as a discipline in itself. We’ll discuss the convergence of people and ideas from diverse fields like Model Theory, Set Theory, Recursion Theory, Proof Theory, Complexity Theory, … that led to the field we know and love today.
- - - - Wednesday, May 18, 2022 - - - -
- - - - Thursday, May 19, 2022 - - - -
- - - - Friday, May 20, 2022 - - - -
Set Theory Seminar
CUNY Graduate Center, Friday, May 20, 12:15pm
In-person: GC Room 6496
Virtual: Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
William Chan, Carnegie Mellon University
Determinacy and Partition Properties
In this talk, we will review some basic properties of partition cardinals under the axiom of determinacy. We will be particularly interested with the strong partition property of the first uncountable cardinal and the good coding system used to derive these partition properties. We will discuss almost everywhere behavior of functions on partition spaces of cardinals with respect to the partition measures including various almost everywhere continuity and monotonicity properties. These continuity results will be used to distinguish some cardinalities below the power set of partition cardinals. We will also use these continuity results to produce upper bounds on the ultrapower of the first uncountable cardinal by each of its partition measures, which addresses a question of Goldberg. Portions of the talk are joint work with Jackson and Trang.
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to
jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email
jreitz@nylogic.org.
Wednesday seminar
Prague Set Theory Seminar
5/8/2022 7:24:01
Dear all,
The seminar meets on Wednesday May 11th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: Jonathan Cancino Manriquez -- Ultrafilters in the Miller model
We will sketch a proof that in the Miller's model I-ultrafilters are
dense in the Rudin-Blass ordering for any analytic tall p-ideal I. We
will finish with some remarks to a theorem of C. Laflamme and J. P. Zhu,
and some questions on cardinal invariants related to the existence of
I-ultrafilters.
Best,
David
Barcelona Set Theory Seminar
Barcelona Logic Seminar
5/7/2022 12:11:27
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: Sandra Müller
TITLE: Inner Models, Determinacy, and Sealing
DATE: 11 May 2022
TIME: 16:00 (CEST)
PLACE: The Seminar will take place online via Zoom:
Meeting ID: 985 6524 7347
Passcode: 243408
Best regards,
Joan
P.S.: If you do not wish to receive any more announcements, please send an email to
bagaria@ub.edu with the text “Unsubscribe”.
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
joan.bagaria@icrea.catbagaria@ub.edu
(KGRC) Wednesday, May 11: Inaugural Lecture of Matthias Aschenbrenner
Kurt Godel Research Center
5/4/2022 11:52:16
The KGRC welcomes as guests:
Miguel Antonio Cardona Montoya (host: Vera Fischer) visits the KGRC until
May 6.
Marta Maloid-Glebova (host: Lyubomyr Zdomskyy) visits the KGRC until May
31.
David Schrittesser (host: Vera Fischer) visits the KGRC until August 31
and gives a talk on June 21. Details for the talk will be announced at a
later time.
James Mitchell (host: Vera Fischer) visits the KGRC from May 21 to May 28.
Yann Peresse (host: Serhii Bardyla) visits the KGRC from May 21 to May 28.
Luke Elliott (host: Lyubomyr Zdomskyy) visits the KGRC from May 21 to May
28.
* * *
Mathematisches Kolloquium
Faculty of Mathematics
Wednesday, May 11
Inaugural Lecture: "Hardy’s dream"
Matthias Aschenbrenner (KGRC)
I will introduce an algebraic approach to asymptotic analysis, which goes
back to G. H. Hardy but has its roots in the 19th century, and which has
found uses in real analytic geometry and dynamical systems, computer
algebra, ergodic theory, and various other fields of mathematics. In the
last few years, we have obtained some decisive results on solving systems
of algebraic differential equations in this setting, leading to rich
classes of non-oscillating differentiable real-valued functions which
partially substantiate “Hardy’s dream” (Ecalle). These results are
obtained through a fruitful interplay between analysis, algebra, and
logic, which I will outline in this talk. (No prior knowledge of
mathematical logic will be assumed.)
Time and Place
Coffee at 3:45pm
Talk at 4:15pm in hybrid mode, in person as well as via Zoom
followed by refreshments
Universität Wien
Fakultät für Mathematik
12th floor
Sky Lounge
Oskar-Morgenstern-Platz 1
1090 Wien
Zoom link for Inaugural Lecture:
https://univienna.zoom.us/j/65619931234?pwd=WTdKV1Z4NGxBeklkT0RtNzltZEhBUT09
(See also PDF attached to this message.)
Tagged: Matthias Aschenbrenner
Mirna Dzamonja at the Toronto Set Theory Seminar
Set Theory Seminar at the Fields Institute
5/2/2022 12:36:28
Morass-generic structures
Speaker:
Mirna Dzamonja, IRIF - Centre national de la recherche scientifique
(CNRS) - Université deParis
Date and Time:
Friday, May 6, 2022 - 1:30pm to 3:00pm EDT (UTC -4)
Location: https://zoom.us/j/92701726800
Abstract:
We discuss a joint work with Wiesław Kubiś on a specific way of
constructing structures of size ℵ1
using finite approximations, namely by organising the approximations
along a simplified morass. We demonstrate a connection with Fraïssé
limits and show that the naturally obtained structure of size ℵ1 is
homogeneous. Moreover, this is preserved under expansions, which leads
us to a partial answer to a question of Bassi and Zucker. We give some
examples of interesting structures constructed, such as the antimetric
space of size ℵ1. Finally, we comment on the situation when one Cohen
real is added.
http://www.fields.utoronto.ca/activities/21-22/set-theory-seminar
This Week in Logic at CUNY
This Week in Logic at CUNY
5/1/2022 22:36:00
This Week in Logic at CUNY:
- - - - Monday, May 2, 2022 - - - -
Logic and Metaphysics Workshop
Date: Monday, May 2, 4.15-6.15 (NY time), GC 5382
For meeting information (including zoom link for those wishing to attend remotely), please sign up for our mailing list at
https://logic.commons.gc.cuny.edu/about/Elia Zardini (Madrid)
Abstract: I’ll first propose an interpretation of the multiplicative/additive distinction among operators arising in a logical framework lacking the structural property of contraction (focusing mostly on the quantifiers): multiplicative operators represent interaction among their operands (with universal quantification representing totality and particular quantification representing dependence) whereas additive operators represent selection (with universal quantification representing choice and particular quantification representing chance). I’ll then argue that reflection on the behaviour of natural-language determiners points towards a very natural working hypothesis that associates: multiplicative universal affirmative with ‘every’; multiplicative particular affirmative with ‘some’; additive universal affirmative with ‘any’; additive particular affirmative with ‘a’. I’ll illustrate the fruitfulness of this hypothesis with four examples, from the epistemic, normative, attitudinal and stative domains respectively.
- - - - Tuesday, May 3, 2022 - - - -
Models of Peano Arithmetic (MOPA)
Tuesday, May 3, 2pm
Virtual (email Victoria Gitman
vgitman@nylogic.org for meeting id)
Dino Rossegger, UC Berkeley and TU Wien
The structural complexity of models of PA
The Scott rank of a countable structure is the least ordinal α such that all automorphism orbits of the structure are definable by infinitary Σα formulas. Montalbán showed that the Scott rank of a structure is a robust measure of the structural and computational complexity of a structure by showing that various different measures are equivalent. For example, a structure has Scott rank α if and only if it has a Πα+1 Scott sentence if and only if it is uniformly ΔΔ0α categorical if and only if all its automorphism orbits are Σα infinitary definable.
In this talk we present results on the Scott rank of non-standard models of Peano arithmetic. We show that non-standard models of PA have Scott rank at least ω, but, other than that, there are no limits to their complexity. Given a completion T of PA we give a reduction via bi-interpretability of the class of linear orders to the models of T. This allows us to exhibit models of T of Scott rank α for every ω≤α≤ω1. In particular, every completion of T has models of high Scott rank.
This is joint work with Antonio Montalbán.
- - - - Wednesday, May 4, 2022 - - - -
The New York City Category Theory Seminar
Department of Computer Science
Department of Mathematics
The Graduate Center of The City University of New York
New URL:
http://www.sci.brooklyn.cuny.edu/~noson/Seminar/index.htmlContact N Yanofsky for zoom info (
noson@sci.brooklyn.cuny.edu)
Speaker: Gershom Bazerman, Arista Networks.
Date and Time: Wednesday May 4, 2022, 7:00 - 8:30 PM., on Zoom.
Title: Classes of Closed Monoidal Functors which Admit Infinite Traversals.
- - - - Thursday, May 5, 2022 - - - -
- - - - Friday, May 6, 2022 - - - -
Set Theory Seminar
CUNY Graduate Center, Friday, May 6, 12:15pm
In-person: GC Room 6496
James Holland Rutgers University
Weak Indestructibility and Reflection
Assuming multiple of strong cardinals, there are lots of cardinals with small degrees of strength (i.e. κ that are κ+2-strong). We can calculate the consistency strength of these all cardinal's small degrees of strength being weakly indestructible using forcing and core model techniques in a way similar to Apter and Sargsyan's previous work. This yields some easy relations between indestructibility and Woodin cardinals, and also generalizes easily to supercompacts. I will give a proof sketches of these results.
Logic Workshop
CUNY Graduate Center, GC Room 6495
Friday, May 6, 2:00-3:30pm
Hybrid - The seminar will take place virtually at 2:00pm US Eastern Standard Time. Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
Alexei Miasnikov, Stevens Institute of Technology
Rich algebraic structures and weak second order logic
“What can one describe by first-order formulas in a given algebraic structure A?” - is an old and interesting question. Of course, this depends on the structure A. For example, in a free group only cyclic subgroups (and the group itself) are definable in the first-order logic, but in a free monoid of finite rank any finitely generated submonoid is definable. An algebraic structure A is called rich if the first-order logic in A is equivalent to the weak second order logic. Surprisingly, there are a lot of interesting groups, rings, semigroups, etc., which are rich. I will discuss some of them and then describe various algebraic, geometric, and algorithmic properties that are first-order definable in rich structures and apply these to some open problems. Weak second order logic can be introduced into algebraic structures in different ways: via HF-logic, or list superstructures over A, or computably enumerable infinite disjunctions and conjunctions, or via finite binary predicates, etc. I will describe a particular form of this logic which is especially convenient to use in algebra and show how to effectively translate such weak second order formulas into the equivalent first-order ones in the case of a rich structure A.
Next Week in Logic at CUNY:
- - - - Monday, May 9, 2022 - - - -
Logic and Metaphysics Workshop
Date: Monday, May 9, 4.15-6.15 (NY time), GC 5382
For meeting information (including zoom link for those wishing to attend remotely), please sign up for our mailing list at
https://logic.commons.gc.cuny.edu/about/Julian Schlöder (UConn).
Title: Neo-Pragmatism about Truth
Abstract: Deflationists about truth hold that the function of the truth predicate is to enable us to make certain assertions we could not otherwise make. Pragmatists claim that the utility of negation lies in its role in registering incompatibility. The pragmatist insight about negation has been successfully incorporated into bilateral theories of content, which take the meaning of negation to be inferentially explained in terms of the speech act of rejection. One can implement the deflationist insight in the pragmatist’s theory of content by taking the meaning of the truth predicate to be explained by its inferential relation to assertion. There are two upshots. First, a new diagnosis of the Liar, Revenges and attendant paradoxes: the paradoxes require that truth rules preserve evidence, but they only preserve commitment. Second, one straightforwardly obtains axiomatisations of several supervaluational hierarchies, answering the question of how such theories are to be naturally axiomatised. This is joint work with Luca Incurvati (Amsterdam).
- - - - Tuesday, May 10, 2022 - - - -
Models of Peano Arithmetic (MOPA)
Tuesday, May 10, 2pm
Virtual (email Victoria Gitman
vgitman@nylogic.org for meeting id)
Saeed Salehi, University of Tabriz
ω-Consistency: Gödel’s “much weaker” notion of soundness
As the history goes, and was confirmed recently [vP20], Gödel first proved his first incompleteness theorem [G31] for sound theories (that extend Principia Mathematica). Later he weakened the soundness condition to “ℵ0-consistency”, which later evolved to “ω-consistency”. This condition was needed for irrefutability of (what is now called) Gödelian sentences; the simple consistency of a theory suffices for the unprovability of such sentences. Gödel already notes in [G31] that a necessary and sufficient condition for the independence of Gödelian sentences of T is just a bit more than the simple consistency of T: the consistency of T with ConT, the consistency statement of T.
In this talk, we ask the following questions and attempt at answering them, at least partially.
- Why on earth Gödel [G31] had to introduce this rather strange notion?
- Does it have any applications in other areas of logic, arithmetical theories, or mathematics?
- What was Gödel’s reason that ω-consistency is “much weaker” than soundness? He does prove in [G31] that consistency is weaker (if not much weaker) than ω-consistency; but never mentions a proof or even a hint as to why soundness is (much) stronger than ω-consistency!
- Other than those historical and philosophical questions, is this a useful notion worthy of further study?
We will also review some properties of ω-consistency in the talk.References:- [G31] Kurt Gödel (1931); “On formally undecidable propositions of Principia Mathematica and related systems I”, in: S. Feferman, et al. (eds.), Kurt Gödel: Collected Works, Vol. I: Publications 1929–1936, Oxford University Press, 1986, pp. 135–152.
- [vP20] Jan von Plato (2020); Can Mathematics Be Proved Consistent? Gödel’s Shorthand Notes & Lectures on Incompleteness, Springer.
Reviewed in the zbMATH Open at https://zbmath.org/1466.03001
- - - - Wednesday, May 11, 2022 - - - -
Tutorial: Categorical Semantics of EntropyWednesday 11 May 2022, 13:00–16:30 Eastern Time, Room 5209 at the CUNY Graduate Center and via Zoom. Organized by John Terilla.
To attend, register here.- - - - Thursday, May 12, 2022 - - - -
- - - - Friday, May 13, 2022 - - - -
Set Theory Seminar
CUNY Graduate Center, Friday, May 13, 12:15pm
In-person: GC Room 6496
Virtual: Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
Andrew Brooke-Taylor University of Leeds
CONFERENCE: Categorical Semantics of Entropy
There will be a workshop on the categorical semantics of entropy at the CUNY Grad Center in Manhattan on Friday May 13th.
John Baez uc Riverside; Centre for Quantum Technologies; Topos Institute
Tai-Danae Bradley The Master's University; Sandbox AQ
Owen Lynch Utrecht University
Tom Mainiero Rutgers New High Energy Theory Center
Arthur Parzygnat Institut des Hautes Études Scientifiques
David Spivak MIT and the Topos Instiftute
Note: There is a related tutorial taking place on May 11 (see above).
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to
jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email
jreitz@nylogic.org.
Wednesday seminar
Prague Set Theory Seminar
4/30/2022 4:39:13
Dear all,
The seminar meets on Wednesday May 4th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: Chris Lambie-Hanson -- Some simple applications of set theory
to the study of projective and injective objects in various categories
Projective and injective objects are of central interest in category
theory and homological algebra. We will survey a few interesting results
applying set-theoretic ideas to the study of such objects in the
categories of compact Hausdorff spaces, Banach spaces, and pro-abelian
groups. Time permitting, we will also discuss some recent applications
of set theory to the newly developed "condensed mathematics" of Clausen
and Scholze. Everything will be presented at a fairly basic level; no
significant prior knowledge of either set theory or category
theory/homological algebra will be required of the audience.
Best,
David
Barcelona Set Theory Seminar
Barcelona Logic Seminar
4/29/2022 5:37:49
Dear All,
For the next seminar session, on May 4, please use the following link, instead of the usual one.
Apologies for the inconvenience.
Best regards,
Joan Bagaria
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: Will Boney
TITLE: Compactness of strong logics and large cardinals
DATE: 4 May 2022
TIME: 16:00 (CET)
PLACE: The Seminar will take place online via Zoom:
Meeting ID: 985 6524 7347
Passcode: 243408
Best regards,
Joan
P.S.: If you do not wish to receive any more announcements, please send an email to
bagaria@ub.edu with the text “Unsubscribe”.
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
joan.bagaria@icrea.catbagaria@ub.edu
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
joan.bagaria@icrea.catbagaria@ub.edu
Barcelona Set Theory Seminar
Barcelona Logic Seminar
4/27/2022 12:10:02
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: Will Boney
TITLE: Compactness of strong logics and large cardinals
DATE: 4 May 2022
TIME: 16:00 (CET)
PLACE: The Seminar will take place online via Zoom:
Meeting ID: 985 6524 7347
Passcode: 243408
Best regards,
Joan
P.S.: If you do not wish to receive any more announcements, please send an email to
bagaria@ub.edu with the text “Unsubscribe”.
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
joan.bagaria@icrea.catbagaria@ub.edu
(KGRC) Set Theory Seminar talk Tuesday, May 3
Kurt Godel Research Center
4/27/2022 9:36:18
The KGRC welcomes as guests:
Marta Maloid-Glebova (host: Lyubomyr Zdomskyy) visits the KGRC from May 2
to May 31.
Miguel Antonio Cardona Montoya (host: Vera Fischer) visits the KGRC from
May 2 to May 6 and gives a talk (see below).
David Schrittesser (host: Vera Fischer) visits the KGRC from May 2 to
August 31 and gives a talk on June 21.
* * *
For a recent session in the Set Theory Research Seminar, video has been
recorded. So if you missed it or want to rewatch it, here it is:
Wolfgang Wohofsky, "Fresh function spectra"
https://univienna.zoom.us/rec/share/vwFTPqrhTaAiFQ69Wn2JQF_nKulP0jvSRK8W3BvInrAyigDfZjMjeV67YOPedR5X.D2QNfwj0OkvjgZID
Passcode H5#My6LX
* * *
Set Theory Research Seminar
Kurt Gödel Research Center
Tuesday, May 3
"On the cardinal characteristics associated with \varepsilon"
Miguel Antonio Cardona Montoya (TU Wien)
Let $\varepsilon$ be the $\sigma$-ideal generated by closed measure zero
sets of reals. We prove that, for $\varepsilon$, their associated cardinal
characteristics (i.e. additivity, covering, uniformity and cofinality) are
pairwise different.
Time and Place
Talk at 3:00pm in hybrid mode, in person as well as via Zoom.
Universität Wien
Institut für Mathematik
Kolingasse 14-16
1090 Wien
1st floor
Seminar room 10
Zoom: If you need the Zoom data and have not received the meeting link by
the day before the talk, please contact richard.springer@univie.ac.at!
(Please direct any other requests about the Set Theory Seminar and its
Zoom meeting to vera.fischer@univie.ac.at.)
Students at Uni Wien are strongly encouraged to attend the seminar in person.
XIX Latin American Symposium of Mathematical Logic (SLALM), Costa Rica, July 26-30
Conference
4/26/2022
Estimado miembro de la comunidad matemática,
Fecha límite extendida para recepción de charlas y pósters: 1 de Mayo del 2022.
Le agradeceríamos difundir a sus colegas, estudiantes y a su Sociedad Matemática local, el anuncio del XIX Simposio Latino Americano de Lógica Matemática, el cual tendrá lugar en la, en la ciudad de San José, Costa Rica, del martes 26 al sábado 30 de Julio del 2022. Esta conferencia será presencial.
Podrá encontrar más información en el siguiente vínculo: Sitio Oficial.
Además, queremos notar las fechas límites:
Inscripción temprana: antes 22 de abril de 2022
Inscripción: antes 30 de junio de 2022
Recepción de charlas contribuidas y pósters: 1° de Mayo, 2022
Comunicación de aceptación-rechazo a los autores: antes 16 de mayo de 2022
Cordialmente,
Comité Organizador
***********************************************************************************************************************************
Extended deadline for contributed talks and posters: May 1st, 2022
Dear member of the mathematical community,
We would be very grateful if you could share with your colleagues, students, and you local Mathematical Society the announcement of the XIX Latin American Symposium of Mathematical Logic (SLALM),
which will be held at the Universidad de Costa Rica, in the city of San José, Costa Rica, from Friday July 26th to Saturday 20th of December, 2022.
You will find more information on the following link: Official website SLALM
Plus, we would like to point out the following important deadlines,
Early registration April 22nd, 2022
Registration: June 30th, 2022
Contributed talks: May 1st, 2022
Communication of acceptance for contributed talks: May 16th, 2022
Sincerely,
Organizing Committee
Tagged: Christina Brech, Deirdre Haskell, Elaine Pimentel, Lluís Godo Lacasa, Matthew Harrison-Trainor, Mrina Dzamonja, Omar León Sánchez, Luiz Carlos Pereira
European Set Theory Conference 2022 - second announcement
Cross-Alps Logic Seminar
4/26/2022 5:46:15
EUROPEAN SET THEORY CONFERENCE 2022
August 29th-September 2nd, 2022
Turin, ItalyThis is the second announcement concerning the
ESTC2022. In particular, please notice that
- The deadline for submitting an abstract is approaching (next Saturday!): if you plan to give a contributed talk, please apply here.
- Various forms of financial support for young researchers are available. We encourage all interested students and young post-docs to apply as soon as possible.
Please share this announcement with all people who might be interested in the event (more information below or on our
website).
We are looking forward to welcoming you in Turin!
Luca Motto Ros (on behalf of the organizers)
-----------------------------------------------
IMPORTANT DEADLINES:
30/04/2022: Abstract submission for contributed talks
30/06/2022: Early registration with reduced fee
22/08/2022: Registration
MORE ON THE CONFERENCE:
The European Set Theory Conferences is a series of biannual meetings coordinated by the European Set Theory Society (ESTS). This year's edition is organized by the Department of Mathematics of the University of Turin and ESTS, in partnership with the Clay Mathematics Institute. It is the most important conference in set theory, and gathers the worldwide leaders in the field as well as many young researchers. During the event, the prestigious Hausdorff medal will be awarded for the most influential work in set theory published in the preceding five years. There will also be a special session in honor of Boban Veličković's 60th birthday.
Invited speakers
- Jeffrey Bergfalk (University of Vienna)
- Filippo Calderoni (University of Illinois Chicago)
- Natasha Dobrinen (University of Denver)
- Osvaldo Guzmán (Universidad Nacional Autónoma de México)
- Joel Hamkins (University of Notre Dame)
- Chris Lambie-Hanson (Czech Academy of Sciences)
- Martino Lupini (Victoria University of Wellington)
- Julien Melleray (Université de Lyon)
- Andrew Marks (University of California, Los Angeles)
- Sandra Müller (TU Wien)
- Saharon Shelah (Hebrew University of Jerusalem)
- Stevo Todorčević (University of Toronto and Centre national de la recherche scientifique)
- Jouko Väänänen (University of Helsinki)
- Zoltán Vidnyánsky (California Institute of Technology)
- Trevor Wilson (Miami University, Oxford Ohio)
Tutorials
- Yair Hayut (Hebrew University of Jerusalem)
- Grigor Sargsyan (Polish Academy of Sciences)
Boban Veličković's 60th Birthday Celebration
- Laura Fontanella (Université Paris-Est Créteil)
- Rahman Mohammadpour (TU Wien)
- Giorgio Venturi (University of Campinas)
- Matteo Viale (University of Turin)
Scientific committee
Joan Bagaria (chair), Matthew Foreman, Moti Gitik, Péter Komjáth, Piotr Koszmider, Heike Mildenberger, Luca Motto Ros, John Steel
Local organizing committee
Alessandro Andretta, Raphaël Carroy, Luca Motto Ros, Gianluca Paolini, Francesco Parente, Salvatore Scamperti, Matteo Viale
--
Luca Motto Ros
Università degli Studi di Torino
Dipartimento di Matematica
via Carlo Alberto, 10 - 10123 Torino, Italy
office phone: (+39) 011 670 2892
fax: (+39) 011 670 2878
Matteo Viale at the Toronto Set Theory Seminar
Set Theory Seminar at the Fields Institute
4/25/2022 13:05:26
The (Absolute) Model Companionship Spectrum of a mathematical theory and
the Continuum problem
Speaker:
Matteo Viale, University of Torino and University of Turin
Date and Time:
Friday, April 29, 2022 - 1:30pm to 3:00pm
Location:
https://zoom.us/j/92701726800
Abstract:
We introduce a classification tool for mathematical theories based on
Robinson's notion of model companionship; roughly the idea is to attach
to a mathematical theory T
those signatures L such that T as axiomatized in L admits a(n absolute)
model companion. To do so we also introduce a slight strengthening of
model companionship (absolute model companionship - AMC) which
characterize those model companionable L-theories T whose model
companion is axiomatized by the Π2-sentences for L which are consistent
with the universal theory of any L-model of T.
We use the above to analyze set theory, and we show that the above
classification tools can be used to extract (surprising?) information on
the continuum problem.
http://www.fields.utoronto.ca/activities/21-22/set-theory-seminar
To unsubscribe, send an email to
SET-THEORY-FIELDS-L-signoff-request@LISTSERV.UTORONTO.CA
This Week in Logic at CUNY
This Week in Logic at CUNY
4/24/2022 22:36:00
This Week in Logic at CUNY:
- - - - Monday, Apr 25, 2022 - - - -
Logic and Metaphysics Workshop
Date: Monday, April 25, 4.15-6.15 (NY time), GC 5382
For meeting information (including zoom link for those wishing to attend remotely), please sign up for our mailing list at
https://logic.commons.gc.cuny.edu/about/Tore Fjetland Øgaard (Bergen).
Title: Logical Suppression Anew
Abstract: Val Plumwood and Richard Sylvan argued from their joint paper The Semantics of First Degree Entailment and onward that the variable sharing property is but a mere consequence of a good entailment relation; indeed they viewed it as a mere negative test of adequacy of such a relation, the property itself being a rather philosophically barren concept. Such a relation is rather to be analyzed as a sufficiency relation free of any form of premise suppression. Suppression of premises, therefore, gained center stage. Despite this, however, no serious attempt was ever made at analyzing the concept. A first rigorous analysis of their notion of suppression was given in Farewell to Suppression-Freedom. Therein it was shown that Plumwood and Sylvan’s notion of suppression is in fact properly weaker than variable sharing. I will in the current talk explore ways of strengthening the suppression criterion. One plausible way of doing so, I will argue, yields a principle equivalent to the standard variable sharing property. I hope to show, then, that the notion of suppression is not as unfruitful as I previously made it out to be.
- - - - Tuesday, Apr 26, 2022 - - - -
Models of Peano Arithmetic (MOPA)
Tuesday, April 26, 2pm
Michał Godziszewski, University of Vienna
Modal Quantifiers, Potential Infinity, and Yablo sequences
When properly arithmetized, Yablo's paradox results in a set of formulas which (with local disquotation in the background) turns out to be consistent, but ω-inconsistent. Adding either uniform disquotation or the ω-rule results in inconsistency. Since the paradox involves an infinite sequence of sentences, one might think that it doesn't arise in finitary contexts. We study whether it does. It turns out that the issue depends on how the finitistic approach is formalized. On one of them, proposed by Marcin Mostowski, all the paradoxical sentences simply fail to hold. This happens at a price: the underlying finitistic arithmetic itself is ω-inconsistent. Finally, when studied in the context of a finitistic approach which preserves the truth of standard arithmetic, the paradox strikes back - it does so with double force, for now the inconsistency can be obtained without the use of uniform disquotation or the ω-rule. This is joint work with Rafał Urbaniak from the University of Gdańsk.
- - - - Wednesday, Apr 27, 2022 - - - -
The New York City Category Theory Seminar
Department of Computer Science
Department of Mathematics
The Graduate Center of The City University of New York
New URL:
http://www.sci.brooklyn.cuny.edu/~noson/Seminar/index.htmlContact N Yanofsky for zoom info (
noson@sci.brooklyn.cuny.edu)
Speaker: Alex Sorokin, Northeastern University.
Date and Time: Wednesday April 27, 2022, 7:00 - 8:30 PM., on Zoom.
Title: The defect of a profunctor.
Abstract: In the mid 1960s Auslander introduced a notion of the defect of a finitely presented functor on a module category. In 2021 Martsinkovsky generalized it to arbitrary additive functors. In this talk I will show how to define a defect of any enriched functor with a codomain a cosmos. Under mild assumptions, the covariant (contravariant) defect functor turns out to be a left covariant (right contravariant) adjoint to the covariant (contravariant) Yoneda embedding. Both defects can be defined for any profunctor enriched in a cosmos V. They happen to be adjoints to the embeddings of V-Cat in V-Prof. Moreover, the Isbell duals of a profunctor are completely determined by the profunctor's covariant and contravariant defects. These results are based on applications of the Tensor-Hom-Cotensor adjunctions and the (co)end calculus.
- - - - Thursday, Apr 28, 2022 - - - -
- - - - Friday, Apr 29, 2022 - - - -
Set Theory Seminar
CUNY Graduate Center, Friday, April 29, 12:15pm
In-person: GC Room 6496
Andreas Blass University of Michigan
Do these ultrafilters exist, II: not Tukey top
This is the second of two talks devoted to two properties of ultrafilters (non-principal, on omega) for which the question 'Do such ultrafilters exist?' is open. In this talk, I'll discuss the property of not being at the top of the Tukey ordering (of ultrafilters on omega). I'll start with the definition of the Tukey ordering, and I'll give an example of an ultrafilter that is 'Tukey top'. It's consistent with ZFC that some ultrafilters are not Tukey top. The examples and the combinatorial characterizations involved here are remarkably similar but not identical to examples and the characterization from the previous talk. That observation suggests some conjectures, one of which I'll disprove if there's enough time.
Next Week in Logic at CUNY:
- - - - Monday, May 2, 2022 - - - -
Logic and Metaphysics Workshop
Date: Monday, May 2, 4.15-6.15 (NY time), GC 5382
For meeting information (including zoom link for those wishing to attend remotely), please sign up for our mailing list at
https://logic.commons.gc.cuny.edu/about/Elia Zardini (Madrid)
- - - - Tuesday, May 3, 2022 - - - -
Models of Peano Arithmetic (MOPA)
Tuesday, May 3, 2pm
Virtual (email Victoria Gitman
vgitman@nylogic.org for meeting id)
Dino Rossegger, UC Berkeley and TU Wien
The structural complexity of models of PA
The Scott rank of a countable structure is the least ordinal α such that all automorphism orbits of the structure are definable by infinitary Σα formulas. Montalbán showed that the Scott rank of a structure is a robust measure of the structural and computational complexity of a structure by showing that various different measures are equivalent. For example, a structure has Scott rank α if and only if it has a Πα+1 Scott sentence if and only if it is uniformly ΔΔ0α categorical if and only if all its automorphism orbits are Σα infinitary definable.
In this talk we present results on the Scott rank of non-standard models of Peano arithmetic. We show that non-standard models of PA have Scott rank at least ω, but, other than that, there are no limits to their complexity. Given a completion T of PA we give a reduction via bi-interpretability of the class of linear orders to the models of T. This allows us to exhibit models of T of Scott rank α for every ω≤α≤ω1. In particular, every completion of T has models of high Scott rank.
This is joint work with Antonio Montalbán.
- - - - Wednesday, May 4, 2022 - - - -
The New York City Category Theory Seminar
Department of Computer Science
Department of Mathematics
The Graduate Center of The City University of New York
New URL:
http://www.sci.brooklyn.cuny.edu/~noson/Seminar/index.htmlContact N Yanofsky for zoom info (
noson@sci.brooklyn.cuny.edu)
Speaker: Gershom Bazerman, Arista Networks.
Date and Time: Wednesday May 4, 2022, 7:00 - 8:30 PM., on Zoom.
Title: Classes of Closed Monoidal Functors which Admit Infinite Traversals.
- - - - Thursday, May 5, 2022 - - - -
- - - - Friday, May 6, 2022 - - - -
Set Theory Seminar
CUNY Graduate Center, Friday, May 6, 12:15pm
In-person: GC Room 6496
James Holland Rutgers University
TBA
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
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jreitz@nylogic.org.
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jreitz@nylogic.org.
Kacper Kucharski, Using elementary submodels in topology (continuation)
IMPAN Working Group in Applications of Set Theory
4/23/2022 5:42:15
Seminar: Working group in applications of set theory, IMPAN
Tuesday, 26.04.2022, at 13.15, room 403
Speaker: Kacper Kucharski, (MIM UW)
Title: Using elementary submodels in topology (continuation)
Abstact: "The talk will be focused on presenting so-called reflection results e.g., Dow's theorem: every nonmetrizable compact Hausdorff space contains a nonmetrizable subspace of cardinality ω_1"
Visit our seminar page which may include some future talks at
https://www.impan.pl/~set_theory/Seminar/
Wednesday seminar
Prague Set Theory Seminar
4/22/2022 6:32:44
Dear all,
The seminar meets on Wednesday April 27th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: Rahman Mohammadpour -- How to specialise a tree with smaller
approximations
A tree T of height $\kappa^+$ is called special if it is
$\kappa$-colorable. The natural forcing to generically specialise a
branchless tree of height $\kappa^+$ uses partial specialising functions
of size less than $\kappa$. The chain condition of the post has a strong
correlation with a particular compactness property. By a classical
result due to Baumgartner, Malitz, and Reinhardt, there is a ccc forcing
notion that generically specialises a branchless tree of height
$\omega_1$, as that compactness property coincides with the property of
being branchless when the height of the tree is $\omega_1$. But when the
height is beyond $\omega_1$, i.e., $\kappa$ is uncountable, there might
be, e.g. in the constructible universe, branchless trees that are not
specialisable at all. Another negative aspect of the specialising poset
is its dependence on cardinal arithmetic. For example, one cannot use it
to generically specialise a tree of height $\omega_2$ without collapsing
the continuum onto $\omega_1$.
I will review some classical and known results on the above subjects. In
particular, the connection between the chain condition of the
specialising poset, the cardinal arithmetic, and a compactness property.
I will then show how to use models, under appropriate circumstances, as
side conditions to arrange specialisation with smaller approximations in
the forcing conditions. I shall first focus on the simplest case, say
trees of height $\omega_2$, and hope that I give enough details of the
proofs. If times permits, I will discuss a similar problem for taller trees.
Best,
David
TOMORROW: Asger Törnquist at 13:30 EDT
Set Theory Seminar at the Fields Institute
4/21/2022 12:16:33
Toronto Set Theory Seminar @ Fields Institute
----------------------------------------------
Friday April 22, 13:30 -- 14:30 EDT (UTC -4)
Asger Törnquist (University of Copenhagen)
Title: The mathematics of a model of the mind in psychology.
Abstract: Jens Mammen, a psychologist, has proposed a model of the human
mind based on the idea that the brain organizes objects in the world
into two kinds of general categories: Broad categories, which he called
"sense categories", and categories of special, distinguished objects (or
people), which he called "choice categories".
From a mathematical point of view, it is interesting that Mammen
formulated his model of the mind axiomatically, based on the notion of a
topological space. The objects in the universe are modelled by the
points in a topological space (U,S), where the (broad) sense categories
are modelled by open sets in the topology S. The choice categories forms
an additional collection of subsets of the universe, C, that together
with the topology must adhere to certain axioms. The triple (U,S,C) is
called a "Mammen space" (a term that I introduced).
Several mathematical questions arise out Mammen's theory. For instance,
if we want Mammen's model to be able to account for all possible subsets
of the universe (a property Mammen called "completeness"), then the
Axiom of Choice, or at least some non-trivial consequences thereof, seem
to play a role. There are also several interesting questions related to
cardinal invariants, such as the "weight" of the underlying topological
space of a complete Mammen space.
I will give an overview of the mathematics of Mammen spaces and known
results, and also discuss the numerous unsolved problems that remain.
location: https://zoom.us/j/92701726800
http://www.fields.utoronto.ca/activities/21-22/set-theory-seminar
This Week in Logic at CUNY
This Week in Logic at CUNY
4/17/2022 22:30:00
This Week in Logic at CUNY:
- - - - Monday, Apr 18, 2022 - - - -
- - - - Tuesday, Apr 19, 2022 - - - -
Models of Peano Arithmetic (MOPA)
Monday, April 19, 2pm
Roman Kossak, CUNY
Absolute undefinability in arithmetic
I will survey some well-known and some more recent undefinability results about models of Peano Arithmetic. I want to contrast first-order undefinability in the standard model with a much stronger notion of undefinability which is suitable for resplendent models, and use the results to motivate some more general questions about the nature of undefinability.
- - - - Wednesday, Apr 20, 2022 - - - -
- - - - Thursday, Apr 21, 2022 - - - -
- - - - Friday, Apr 22, 2022 - - - -
Set Theory Seminar
CUNY Graduate Center, Friday, April 22, 12:15pm
In-person: GC Room 6496
Andreas Blass University of Michigan
Logic Workshop
CUNY Graduate Center, Friday, April 22, 2pm
In Person (contact Russell Miller by April 15 to be admitted into GC for the talk)
GC Room 5417
Jouko Väänänen University of Helsinki
Stationary logic and set theory
Stationary logic was introduced in the 1970’s. It allows the quantifier 'for almost all countable subsets s…'. Although it is undoubtedly a kind of second order logic, it is completely axiomatizable, countably compact and satisfies a kind of Downward Lowenheim-Skolem theorem. In this talk I give first a general introduction to the extension of first order logic by this 'almost all'-quantifier. As 'almost all' is interpreted as 'for a club of', the theory of this logic is entangled with properties of stationary sets. I will give some examples of this. The main reason to focus on this logic in my talk is to use it to build an inner model of set theory. I will give a general introduction to this inner model, called C(aa), or the aa-model, and sketch a proof of CH in the model. My work on the aa-model is joint work with Juliette Kennedy and Menachem Magidor.
Next Week in Logic at CUNY:
- - - - Monday, Apr 25, 2022 - - - -
- - - - Tuesday, Apr 26, 2022 - - - -
Models of Peano Arithmetic (MOPA)
Monday, April 26, 2pm
Michał Godziszewski, University of Vienna
Modal Quantifiers, Potential Infinity, and Yablo sequences
When properly arithmetized, Yablo's paradox results in a set of formulas which (with local disquotation in the background) turns out to be consistent, but ω-inconsistent. Adding either uniform disquotation or the ω-rule results in inconsistency. Since the paradox involves an infinite sequence of sentences, one might think that it doesn't arise in finitary contexts. We study whether it does. It turns out that the issue depends on how the finitistic approach is formalized. On one of them, proposed by Marcin Mostowski, all the paradoxical sentences simply fail to hold. This happens at a price: the underlying finitistic arithmetic itself is ω-inconsistent. Finally, when studied in the context of a finitistic approach which preserves the truth of standard arithmetic, the paradox strikes back - it does so with double force, for now the inconsistency can be obtained without the use of uniform disquotation or the ω-rule. This is joint work with Rafał Urbaniak from the University of Gdańsk.
- - - - Wednesday, Apr 27, 2022 - - - -
- - - - Thursday, Apr 28, 2022 - - - -
- - - - Friday, Apr 29, 2022 - - - -
Set Theory Seminar
CUNY Graduate Center, Friday, April 29, 12:15pm
In-person: GC Room 6496
Andreas Blass University of Michigan
- - - - Other Logic News - - - -
CONFERENCE ANNOUNCEMENT:
Logic4Peace: fundraising online Logic event for Peace
University of Amsterdam
Dates: 22 and 23 April 2022
Venue: online (information will be provided to registered participants)
Logicians participating in this conference stand united for Peace. The on-going Russian military invasion in Ukraine is causing death, destruction and it is the direct cause of a gigantic humanitarian crisis. Educational facilities have been hit, supply chains have been broken and people have lost their families and homes. By organizing this conference, we offer our moral and financial support to our colleagues in Ukraine in this time of war.
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
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CMU seminars this week (logic, model theory, set theory)
Carnegie Mellon Logic Seminar
4/16/2022 9:18:03
TUESDAY, April 19, 2022
Mathematical logic seminar: 3:30 P.M., Online, Samson Leung, Carnegie
Mellon University
Join Zoom Meeting:
https://cmu.zoom.us/j/92655324096?pwd=VUhSSlkrdHMxbTlSYUMxYzFXM01kdz09
Meeting ID: 926 5532 4096
Passcode: 555455
TITLE: Categoricity results of abstract elementary classes (Part I)
ABSTRACT: The notion of abstract elementary classes (AECs) is an axiomatic
framework developed by Shelah to generalize classification theory beyond
the first-order context. One central test question is the categoricity
conjecture: if an AEC K is categorical in some
$\mu\geq\beth_{(2^{LS(K)})^+}$, then it is categorical in all
$\mu\geq\beth_{(2^{LS(K)})^+}$. After going through the axioms of AECs, we
will overview some partial results in the literature, in particular those
assuming tameness, type-shortness and the amalgamation property. We show
that: assuming type-shortness and amalgamation over sets, the categoricity
conjecture is true. Our result also provides an alternative proof to the
upward categoricity transfer in first-order theories.
TUESDAY, April 19, 2022
Set Theory Seminar: 4:30 P.M., Online, Samson Leung, Carnegie
Mellon University
Join Zoom Meeting:
https://cmu.zoom.us/j/92655324096?pwd=VUhSSlkrdHMxbTlSYUMxYzFXM01kdz09
Meeting ID: 926 5532 4096
Passcode: 555455
TITLE: Categoricity results of abstract elementary classes (Part II)
ABSTRACT: We will look at the main tools used in the proof of our
categoricity transfer: good frames, multidimensional diagrams and primes.
It is known that our assumptions allow a set-theoretic argument to
transfer categoricity down to $\beth_{(2^{LS(K)})^+}$. We will discuss
examples that encode the cumulative hierarchy, which have the first
categoricity cardinals up to $\beth_{(2^{LS(K)})^+}$, but fail
amalgamation. We conjecture that a more refined set-theoretic construction
might provide such examples that also satisfy amalgamation, which will
imply the above threshold is tight.
THURSDAY, April 21, 2022
Model Theory Seminar: 11:00 A.M., Online, T. G. Kucera, University of
Manitoba, Canada
Join Zoom Meeting:
https://cmu.zoom.us/j/96301869290?pwd=Qk1zS0h6ZThmUnRpbmNLNkVJSjkrQT09
Meeting ID: 963 0186 9290
Passcode: 567655
TITLE: Saturated free algebras and almost indiscernible theories: an
overview
ABSTRACT: This is work motivated by questions at the intersection of
algebra and model theory, and using advanced techniques of model theory.
Baldwin and Shelah (Algebra Universalis, 1983) studied saturated free
algebras. Pillay and Sklinos (Bull. Symb. Logic 2015), following the lead
of this paper, studied "almost indiscernible theories", taking the
opportunity to refine the statements of the major results and improve the
proofs. We extend these results to large infinite contexts, both in the
size of the language and the kinds of tuples allowed in an indiscernible
set, and return to examples and applications in algebra, in particular in
the theory of modules.
The theory develops by noting various analogies. The idea of
'indiscernible sequence' generalizes various kinds of independence in
algebra, including 'linearly independent set' in a vector space, 'free
(generating) set' of an algebra, 'algebraic independence' in an
algebraically closed field, and similar concepts. 'Saturated model'
generalizes concepts such as 'injective envelope of a module', 'algebraic
closure of a field', and similar constructions. A complete theory is
"almost indiscernible" if it has a (sufficiently large) saturated model
which lies in the algebraic closure of an indiscernible set (of
sequences). Requiring that a saturated model be generated by an
indiscernible set imposes strong structural constraints, but nonetheless
there are natural motivating examples. This will be a talk without proofs.
If there is sufficient interest I can return at a later time to cover the
proofs of the main model-theoretic results.
I start with some history and motivation from algebra, and then introduce
our extension of the definition of an "almost indiscernible theory". I
will give a summary of the main results, in particular that such a theory
T is superstable, stable in |T|, and non-multi-dimensional. I'll only
mention briefly the main tools of the proofs.
Then I will present some consequences for free algebras and for theories
of modules, including structure theorems and some examples.
I conclude with a list of open questions.
This is joint work with Anand Pillay
Article link: https://link.springer.com/article/10.1007/s00012-021-00766-x
Wednesday seminar
Prague Set Theory Seminar
4/16/2022 7:15:02
Dear all,
The seminar meets on Wednesday April 20th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: Claudio Agostini -- On some extensions of theorems in combinatorics
Ramsey monoids have been introduced by Solecki in 2019 to generalize and
extend famous theorems in combinatorics such as Hindman’s theorem,
Carlson’s Theorem on variable words, and Gowers’ $\mathrm{FIN}_k$
Theorem. In short, a monoid is Ramsey if for every action of the monoid
on a semigroup and for any finite coloring of the semigroup there is an
infinite monochromatic ``nice set'' closed to a certain degree under the
operation of the semigroup and the action of the monoid. Relaxing or
strengthening the requirements that the ``nice set'' must satisfies, one
can obtain other classes of monoids, like $\mathbb{Y}$-controllable
monoids, locally Ramsey monoids and locally $\mathbb{Y}$-controllable
monoids.
In this talk, I will introduce these notions and discuss some recent
progress in the study of these classes.
This is a joint work with Eugenio Colla.
Best,
David
Wednesday seminar
Prague Set Theory Seminar
4/11/2022 5:39:15
Dear all,
The seminar meets on Wednesday April 13th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: David Chodounsky -- Colors of the pseudotree
The pseudotree is the Fraisse limit of the class of finite trees with
embeddings which respect the meet operation. In this short talk I will
cover the little we know about the big Ramsey degrees of substructures
of the pseudotree.
This is joint work Monroe Eskew and Thilo Weinert.
Best,
David
This Week in Logic at CUNY
This Week in Logic at CUNY
4/10/2022 22:31:00
This Week in Logic at CUNY:
- - - - Monday, Apr 11, 2022 - - - -
Logic and Metaphysics Workshop
Date: Monday, April 11, 4.15-6.15 (NY time), GC 5382
For meeting information (including zoom link for those wishing to attend remotely), please sign up for our mailing list at
https://logic.commons.gc.cuny.edu/about/Justin Bledin (Johns Hopkins)
Title: From Truthmaker to Menu Semantics
Abstract: The logical foundations of English and other natural languages are often assumed to have an essentially truth-theoretic character where the meanings of connectives and quantifiers are grounded in the truth and falsity of sentences. In this talk, I explore a fundamentally different perspective that shifts the focus from the truth value to the ‘menu’. Under this alternative conception of the logic of natural language, speakers manifest their logical competence by, metaphorically speaking, constructing and combining menus of items in various types throughout the grammar. The logical connectives are ‘menu constructors’: negation can be used to express that items are ‘off’ the menu, conjunction produces combinations of ‘on-menu’ items, and disjunction introduces choice between items. My point of departure for this truth displacing project is, oddly enough, recent work in ‘truthmaker’ or ‘exact’ semantics. What I try to do is build a bridge between the standard theory of truthmaker semantics (van Fraassen 1969; Fine 2017), which assigns menus of truthmakers and falsemakers at the sentential level, and compositional semantics in the general style of Montague. One of the most striking aspects of the theory is its treatment of noun phrases, as both quantificational and non-quantificational NPs are all assigned both denotations and ‘anti-denotations’ drawn or constructed from a rich entity space populated by both positive and negative individuals and their sums. Towards the end of the talk, I will try to bring out the explanatory power of menu semantics by applying it to a couple of problem areas in natural language quantification.
- - - - Tuesday, Apr 12, 2022 - - - -
Models of Peano Arithmetic (MOPA)
Monday, April 12, 2pm
Thomas Ferguson University of Amsterdam and University of St. Andrews
Speaker: Alex Martsinkovsky, Northeastern University.
Date and Time: Wednesday April 13, 2022, 7:00 - 8:30 PM., on Zoom.
Title: A Reflector in Search of a Category.
Abstract: The last several months have seen an explosive growth of activities centered around the defect of a finitely presented functor. This notion made its first appearance in M. Auslander's fundamental work on coherent functors in the mid-1960s, although at that time it was mostly used just as a technical tool. A phenomenological study of that concept was initiated by Jeremy Russell in 2016. What transpired in the recent months is the ubiquitous nature of the defect, explained in part by the fact that it is adjoint to the Yoneda embedding. Thus any branch of mathematics, computer science, physics, or any applied science that references the Yoneda embedding automatically becomes a candidate for applications of the defect.
In this expository talk I will first give a streamlined introduction to the original notion of defect of a finitely presented functor defined on a module category and then show how to generalize it to arbitrary additive functors. Along the way I will give a dozen or so examples illustrating various use cases for the defect. The ultimate goal of this lecture is to provide a background for the upcoming talk of Alex Sorokin, who will report on his vast generalization of the defect to arbitrary profunctors enriched in a cosmos.
This presentation is based on joint work in progress with Jeremy Russell.
- - - - Thursday, Apr 14, 2022 - - - -
- - - - Friday, Apr 15, 2022 - - - -
Set Theory Seminar
CUNY Graduate Center, Friday, April 15, 12:15pm
In-person: GC Room 6496
The surprising strength of reflection in second-order set theory with abundant urelements
I shall give a general introduction to urelement set theory and the role of the second-order reflection principle in second-order urelement set theory GBCU and KMU. With the abundant atom axiom, asserting that the class of urelements greatly exceeds the class of pure sets, the second-order reflection principle implies the existence of a supercompact cardinal in an interpreted model of ZFC. The proof uses a reflection characterization of supercompactness: a cardinal κ is supercompact if and only if for every second-order sentence true in some structure M (of any size) is also true in a first-order elementary substructure m≺M of size less than κ. This is joint work with Bokai Yao. http://jdh.hamkins.org/surprising-strength-of-reflection-with-abundant-urelements-cuny-set-theory-seminar-april-2022
Next Week in Logic at CUNY:
- - - - Monday, Apr 18, 2022 - - - -
- - - - Tuesday, Apr 19, 2022 - - - -
Models of Peano Arithmetic (MOPA)
Monday, April 19, 2pm
Roman Kossak, CUNY
Absolute undefinability in arithmetic
I will survey some well-known and some more recent undefinability results about models of Peano Arithmetic. I want to contrast first-order undefinability in the standard model with a much stronger notion of undefinability which is suitable for resplendent models, and use the results to motivate some more general questions about the nature of undefinability.
- - - - Wednesday, Apr 20, 2022 - - - -
- - - - Thursday, Apr 21, 2022 - - - -
- - - - Friday, Apr 22, 2022 - - - -
Set Theory Seminar
CUNY Graduate Center, Friday, April 22, 12:15pm
In-person: GC Room 6496
Andreas Blass University of Michigan
Logic Workshop
CUNY Graduate Center, Friday, April 22, 2pm
In-person only: CUNY Graduate Center Room 6496
Jouko Väänänen University of Helsinki
- - - - Other Logic News - - - -
CONFERENCE ANNOUNCEMENT:
Logic4Peace: fundraising online Logic event for Peace
University of Amsterdam
Dates: 22 and 23 April 2022
Venue: online (information will be provided to registered participants)
Logicians participating in this conference stand united for Peace. The on-going Russian military invasion in Ukraine is causing death, destruction and it is the direct cause of a gigantic humanitarian crisis. Educational facilities have been hit, supply chains have been broken and people have lost their families and homes. By organizing this conference, we offer our moral and financial support to our colleagues in Ukraine in this time of war.
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
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jreitz@nylogic.org.
Upcoming seminars (logic, model theory, set theory)
Carnegie Mellon Logic Seminar
4/8/2022 12:15:20
TUESDAY, April 12, 2022
Mathematical logic seminar: 3:30 P.M., Online, Garrett Ervin, Carnegie
Mellon University
Join Zoom Meeting:
https://cmu.zoom.us/j/92655324096?pwd=VUhSSlkrdHMxbTlSYUMxYzFXM01kdz09
Meeting ID: 926 5532 4096
Passcode: 555455
TITLE: Filter flows
ABSTRACT: A directed hypergraph G consists of a vertex set V along with a
collection of directed hyperedges (A, B), where A and B are finite subsets
of V. Given a set of vertices X, we think of the edge (A, B) as being on
the boundary of X if X intersects A and does not completely contain B.
We can generalize the notion of directed hypergraph as follows. A _filter
graph_ G consists of an infinite vertex set V along with a collection of
edges (F, G), where F and G are filters on V. Given a set of vertices X,
we think of the edge (F, G) as being on the boundary of X if X is
F-positive and the complement of X is G-positive.
Filter graphs seem to be surprisingly graph-like. We'll show in this talk
that filter graphs satisfy the natural generalization of the
max-flow/min-cut theorem, where point masses flowing along directed edges
in the usual hypergraph setting are replaced by ultrafilters flowing along
filter-edges.
TUESDAY, April 19, 2022
Mathematical logic seminar: 3:30 P.M., Online, Samson Leung, Carnegie
Mellon University
Join Zoom Meeting:
https://cmu.zoom.us/j/92655324096?pwd=VUhSSlkrdHMxbTlSYUMxYzFXM01kdz09
Meeting ID: 926 5532 4096
Passcode: 555455
TITLE: Categoricity results of abstract elementary classes (Part I)
ABSTRACT: The notion of abstract elementary classes (AECs) is an axiomatic
framework developed by Shelah to generalize classification theory beyond
the first-order context. One central test question is the categoricity
conjecture: if an AEC K is categorical in some
$\mu\geq\beth_{(2^{LS(K)})^+}$, then it is categorical in all
$\mu\geq\beth_{(2^{LS(K)})^+}$. After going through the axioms of AECs, we
will overview some partial results in the literature, in particular those
assuming tameness, type-shortness and the amalgamation property. We show
that: assuming type-shortness and amalgamation over sets, the categoricity
conjecture is true. Our result also provides an alternative proof to the
upward categoricity transfer in first-order theories.
TUESDAY, April 19, 2022
Set Theory Reading Group: 4:30 P.M., Online, Samson Leung, Carnegie
Mellon University
Join Zoom Meeting:
https://cmu.zoom.us/j/92655324096?pwd=VUhSSlkrdHMxbTlSYUMxYzFXM01kdz09
Meeting ID: 926 5532 4096
Passcode: 555455
TITLE: Categoricity results of abstract elementary classes (Part II)
ABSTRACT: We will look at the main tools used in the proof of our
categoricity transfer: good frames, multidimensional diagrams and primes.
It is known that our assumptions allow a set-theoretic argument to
transfer categoricity down to $\beth_{(2^{LS(K)})^+}$. We will discuss
examples that encode the cumulative hierarchy, which have the first
categoricity cardinals up to $\beth_{(2^{LS(K)})^+}$, but fail
amalgamation. We conjecture that a more refined set-theoretic construction
might provide such examples that also satisfy amalgamation, which will
imply the above threshold is tight.
THURSDAY, April 21, 2022
Model Theory Seminar: 11:00 A.M., Online, T. G. Kucera, University of
Manitoba, Canada
Join Zoom Meeting:
https://cmu.zoom.us/j/96301869290?pwd=Qk1zS0h6ZThmUnRpbmNLNkVJSjkrQT09
Meeting ID: 963 0186 9290
Passcode: 567655
TITLE: Saturated free algebras and almost indiscernible theories: an
overview
ABSTRACT: This is work motivated by questions at the intersection of
algebra and model theory, and using advanced techniques of model theory.
Baldwin and Shelah (Algebra Universalis, 1983) studied saturated free
algebras. Pillay and Sklinos (Bull. Symb. Logic 2015), following the lead
of this paper, studied "almost indiscernible theories", taking the
opportunity to refine the statements of the major results and improve the
proofs. We extend these results to large infinite contexts, both in the
size of the language and the kinds of tuples allowed in an indiscernible
set, and return to examples and applications in algebra, in particular in
the theory of modules.
The theory develops by noting various analogies. The idea of
'indiscernible sequence' generalizes various kinds of independence in
algebra, including 'linearly independent set' in a vector space, 'free
(generating) set' of an algebra, 'algebraic independence' in an
algebraically closed field, and similar concepts. 'Saturated model'
generalizes concepts such as 'injective envelope of a module', 'algebraic
closure of a field', and similar constructions. A complete theory is
"almost indiscernible" if it has a (sufficiently large) saturated model
which lies in the algebraic closure of an indiscernible set (of
sequences). Requiring that a saturated model be generated by an
indiscernible set imposes strong structural constraints, but nonetheless
there are natural motivating examples.
This will be a talk without proofs. If there is sufficient interest I can
return at a later time to cover the proofs of the main model-theoretic
results.
I start with some history and motivation from algebra, and then introduce
our extension of the definition of an "almost indiscernible theory". I
will give a summary of the main results, in particular that such a theory
T is superstable, stable in |T|, and non-multi-dimensional. I'll only
mention briefly the main tools of the proofs.
Then I will present some consequences for free algebras and for theories
of modules, including structure theorems and some examples.
I conclude with a list of open questions.
This is joint work with Anand Pillay
Article link: https://link.springer.com/article/10.1007/s00012-021-00766-x
THURSDAY, April 28, 2022
Model Theory Seminar: 11:00 A.M., Online, Jonathan Kirby, The University
of East Anglia
Join Zoom Meeting:
https://cmu.zoom.us/j/96301869290?pwd=Qk1zS0h6ZThmUnRpbmNLNkVJSjkrQT09
Meeting ID: 963 0186 9290
Passcode: 567655
TITLE: Independence Relations for Exponential Fields
ABSTRACT: In classical first-order logic, the presence of an independence
relation on models of a complete theory T can be used to show that T is
strongly minimal, stable, simple, or NSOP_1. Something analogous works in
various generalisations of first-order logic, including AECs.
In this talk I will illustrate the general principle by constructing
various independence relations on exponential fields, that is, fields
equipped with a homomorphism from their additive group to their
multiplicative group, like the usual real and complex exponential maps.
These independence relations can be used to prove that various AECs of
exponential fields are quasiminimal, stable, or NSOP_1.
In some of the stable cases, there are open questions around extending
from the countable models, which are well-understood, to the uncountable
ones.
This is joint work with Levon Haykazyan, Robert Henderson, Mark Kamsma,
and Vahagn Aslanyan.
Logic Seminar 13 April 2022 16:00 hrs at NUS by Wang Wei, Sun Yatsen University
NUS Logic Seminar
4/8/2022 4:59:48
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 13 April 2022, 16:00 hrs
Talk via Zoom:
https://nus-sg.zoom.us/j/83049258042?pwd=UWViaWNvTFUrdFdhOHJCdEVydnVkdz09
Meeting ID: 830 4925 8042
Passcode: 1729=x3+y3
Speaker: Wang Wei
Title: Ackermann, Ramsey and Trees
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Recently, Chong, Yang and I prove that a version of Pigeonholes Principle
for trees (TT^1) is Pi^0_3-conservative over RCA_0.
So, TT^1 does not imply the totality of Ackermann function over RCA_0,
like the instance of Ramsey's Theorem for 2-colorings of pairs.
To fit the trend of logic talks, I am not going to present many details.
Instead, I will try to recall some stories about the Ackermann function and its
appearance in reverse mathematics.
Logic Seminar 6 April 2022 16:00 hrs by Frank Stephan, NUS
NUS Logic Seminar
4/6/2022 3:58:46
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 6 April 2022, 16:00 hrs
Talk via Zoom:
https://nus-sg.zoom.us/j/83049258042?pwd=UWViaWNvTFUrdFdhOHJCdEVydnVkdz09
Meeting ID: 830 4925 8042
Passcode: 1729=x3+y3
Speaker: Frank Stephan
Title: Matching Regular Pumping Lemmas and Automaticity
Abstract: The talk investigates which versions of the pumping
lemma are matching where matching means that exactly the regular
languages satisfy it. In particular it will be shown that
two-sided pumping lemmas where an automatic function computes
the pump tend to be matching.
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Cross-Alps Logic Seminar (speaker: Alexander S. Kechris)
Cross-Alps Logic Seminar
4/5/2022 1:48:30
On Friday 08.04.2022 at 16:00 CEST
Alexander S. Kechris (Caltech)
will give a talk on
Countable sections for actions of locally compact groups
Please refer to the usual webpage of our
LogicGroup
for more details and the abstract of the talk.
The seminar will be held remotely through Webex. Please write to
luca.mottoros [at] unito [dot] itfor the link to the event.
The Cross-Alps Logic Seminar is co-organized by the logic groups of
Genoa, Lausanne, Turin and Udine as part of our collaboration in the
project PRIN 2017 'Mathematical logic: models, sets, computability'.
This Week in Logic at CUNY
This Week in Logic at CUNY
4/3/2022 22:30:00
This Week in Logic at CUNY:
- - - - Monday, Apr 4, 2022 - - - -
Logic and Metaphysics WorkshopDate: Monday, April 4, 4.15-6.15 (NY time), GC 5382For meeting information (including zoom link for those wishing to attend remotely), please sign up for our mailing list at https://logic.commons.gc.cuny.edu/about/Jenn McDonald (Columbia)
Title: Causal Relativism
Abstract: In this talk, I defend a kind of causal relativism. I argue that actual causation cannot be taken to hold simpliciter between two particular things (‘things’ such as events, states-of-affairs, etc.). Instead, actual causation holds only relative to a background space of possibilities – a modal profile. The argument applies generally to any difference-making analysis of actual causation. But I will use the framework of structural equation models to make the case. I first demonstrate that structural equation models represent situations in this way – as relative to some modal profile or other. This observation is underappreciated in the literature. I show how it raises a problem for all extant analyses of actual causation in terms of these models. This problem is best responded to by a kind of causal relativism, or so I will argue. Notably, the problem cannot be avoided by rejecting a structural equation framework. While the framework is useful for its illustration, the problem arises for any analysis governed by the idea that a cause is what makes a difference in an effect’s occurrence.
Speaker: Jason Parker, Brandon University in Manitoba.
Date and Time: Wednesday April 6, 2022, 7:00 - 8:30 PM., on Zoom.
Title: Enriched structure-semantics adjunctions and monad-theory equivalences for subcategories of arities.
Abstract: Several structure-semantics adjunctions and monad-theory equivalences have been established in category theory. Lawvere (1963) developed a structure-semantics adjunction between Lawvere theories and tractable Set-valued functors, which was subsequently generalized by Linton (1969), while Dubuc (1970) established a structure-semantics adjunction between V-theories and tractable V-valued V-functors for a symmetric monoidal closed category V. It is also well known (and due to Linton) that there is an equivalence between Lawvere theories and finitary monads on Set. Generalizing this result, Lucyshyn-Wright (2016) established a monad-theory equivalence for eleutheric systems of arities in arbitrary closed categories. Building on earlier work by Nishizawa and Power, Bourke and Garner (2019) subsequently proved a general monad-theory equivalence for arbitrary small subcategories of arities in locally presentable enriched categories. However, neither of these equivalences generalizes the other, and there has not yet been a general treatment of enriched structure-semantics adjunctions that specializes to those established by Lawvere, Linton, and Dubuc.
Motivated by these considerations, we develop a general axiomatic framework for studying enriched structure-semantics adjunctions and monad-theory equivalences for subcategories of arities, which generalizes all of the aforementioned results and also provides substantial new examples of relevance for topology and differential geometry. For a subcategory of arities J in a V-category C over a symmetric monoidal closed category V, Linton’s notion of clone generalizes to provide enriched notions of J-theory and J-pretheory, which were also employed by Bourke and Garner (2019). We say that J is amenable if every J-theory admits free algebras, and is strongly amenable if every J-pretheory admits free algebras. If J is amenable, then we obtain an idempotent structure-semantics adjunction between certain J-pretheories and J-tractable V-categories over C, which yields an equivalence between J-theories and J-nervous V-monads on C. If J is strongly amenable, then we also obtain a rich theory of presentations for J-theories and J-nervous V-monads. We show that many previously studied subcategories of arities are (strongly) amenable, from which we recover the aforementioned structure-semantics adjunctions and monad-theory equivalences. We conclude with the result that any small subcategory of arities in a locally bounded closed category is strongly amenable, from which we obtain structure-semantics adjunctions and monad-theory equivalences in (e.g.) many convenient categories of spaces.
Joint work with Rory Lucyshyn-Wright.
- - - - Thursday, Apr 7, 2022 - - - -
- - - - Friday, Apr 8, 2022 - - - -
Next Week in Logic at CUNY:
- - - - Monday, Apr 11, 2022 - - - -
Logic and Metaphysics Workshop
Date: Monday, April 11, 4.15-6.15 (NY time), GC 5382
For meeting information (including zoom link for those wishing to attend remotely), please sign up for our mailing list at
https://logic.commons.gc.cuny.edu/about/Justin Bledin (Johns Hopkins)
Title: From Truthmaker to Menu Semantics
Abstract: The logical foundations of English and other natural languages are often assumed to have an essentially truth-theoretic character where the meanings of connectives and quantifiers are grounded in the truth and falsity of sentences. In this talk, I explore a fundamentally different perspective that shifts the focus from the truth value to the ‘menu’. Under this alternative conception of the logic of natural language, speakers manifest their logical competence by, metaphorically speaking, constructing and combining menus of items in various types throughout the grammar. The logical connectives are ‘menu constructors’: negation can be used to express that items are ‘off’ the menu, conjunction produces combinations of ‘on-menu’ items, and disjunction introduces choice between items. My point of departure for this truth displacing project is, oddly enough, recent work in ‘truthmaker’ or ‘exact’ semantics. What I try to do is build a bridge between the standard theory of truthmaker semantics (van Fraassen 1969; Fine 2017), which assigns menus of truthmakers and falsemakers at the sentential level, and compositional semantics in the general style of Montague. One of the most striking aspects of the theory is its treatment of noun phrases, as both quantificational and non-quantificational NPs are all assigned both denotations and ‘anti-denotations’ drawn or constructed from a rich entity space populated by both positive and negative individuals and their sums. Towards the end of the talk, I will try to bring out the explanatory power of menu semantics by applying it to a couple of problem areas in natural language quantification.
- - - - Tuesday, Apr 12, 2022 - - - -
Models of Peano Arithmetic (MOPA)
Monday, April 12, 2pm
Thomas Ferguson University of Amsterdam and University of St. Andrews
Speaker: Alex Martsinkovsky, Northeastern University.
Date and Time: Wednesday April 13, 2022, 7:00 - 8:30 PM., on Zoom.
Title: A Reflector in Search of a Category.
Abstract: The last several months have seen an explosive growth of activities centered around the defect of a finitely presented functor. This notion made its first appearance in M. Auslander's fundamental work on coherent functors in the mid-1960s, although at that time it was mostly used just as a technical tool. A phenomenological study of that concept was initiated by Jeremy Russell in 2016. What transpired in the recent months is the ubiquitous nature of the defect, explained in part by the fact that it is adjoint to the Yoneda embedding. Thus any branch of mathematics, computer science, physics, or any applied science that references the Yoneda embedding automatically becomes a candidate for applications of the defect.
In this expository talk I will first give a streamlined introduction to the original notion of defect of a finitely presented functor defined on a module category and then show how to generalize it to arbitrary additive functors. Along the way I will give a dozen or so examples illustrating various use cases for the defect. The ultimate goal of this lecture is to provide a background for the upcoming talk of Alex Sorokin, who will report on his vast generalization of the defect to arbitrary profunctors enriched in a cosmos.
This presentation is based on joint work in progress with Jeremy Russell.
- - - - Thursday, Apr 14, 2022 - - - -
- - - - Friday, Apr 15, 2022 - - - -
Set Theory Seminar
CUNY Graduate Center, Friday, April 1, 12:15pm
In-person: GC Room 6496
Joel David Hamkins Notre Dame University
- - - - Other Logic News - - - -
CONFERENCE ANNOUNCEMENT:
Logic4Peace: fundraising online Logic event for Peace
University of Amsterdam
Dates: 22 and 23 April 2022
Venue: online (information will be provided to registered participants)
Logicians participating in this conference stand united for Peace. The on-going Russian military invasion in Ukraine is causing death, destruction and it is the direct cause of a gigantic humanitarian crisis. Educational facilities have been hit, supply chains have been broken and people have lost their families and homes. By organizing this conference, we offer our moral and financial support to our colleagues in Ukraine in this time of war.
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to
jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email
jreitz@nylogic.org.
Damian Sobota, Measures with the Additive Property and the random forcing
IMPAN Working Group in Applications of Set Theory
4/3/2022 11:14:04
Seminar: Working group in applications of set theory, IMPAN
Tuesday, 5.04.2022, at 13.15, room 403
Speaker: Damian Sobota, (KGRC Vienna)
Title: Measures with the Additive Property and the random forcing
Abstact: "Let μ be a finitely additive probability measure on ω which vanishes on points, that is, μ({n})=0 for every n∈ω. It follows immediately that μ is not σ-additive, however it may be almost σ-additive in the following weak sense. We say that μ has the Additive Property, (AP) in short, if for every sequence (A_n) of pairwise disjoint subsets of ω there is a subset A such that A_n\A is finite for every n∈ω and μ(A)=Σ_n μ(A_n). Equivalently, for every decreasing sequence (A_n) of subsets of ω there is a subset A such that A\A_n is finite for every n∈ω and μ(A)=lim_n μ(A_n). The latter definition implies immediately that, e.g., an ultrafilter U on ω is a P-point if and only if the one-point measure δ_U has (AP). And similarly as in the case of P-points the existence of measures with (AP) is independent of ZFC.
During my talk I will discuss basic properties of (families of) measures with (AP) as well as show, at least briefly, that using old ideas of Solovay and Kunen one can obtain a non-atomic measure with (AP) in the random model. The latter result implies that in this model there exists a ccc P-set in ω*, which may be treated as a (weak) partial answer to the question asking whether there are P-points in the random model.
This is a joint work with Piotr Borodulin-Nadzieja."
Visit our seminar page which may include some future talks at
https://www.impan.pl/~set_theory/Seminar/
Next math logic seminar on Tuesday
Carnegie Mellon Logic Seminar
4/1/2022 13:03:24
TUESDAY, April 5, 2022
Mathematical logic seminar: 3:30 P.M., Online, Benjamin Siskind, Carnegie
Mellon University
Join Zoom Meeting:
https://cmu.zoom.us/j/92655324096?pwd=VUhSSlkrdHMxbTlSYUMxYzFXM01kdz09
Meeting ID: 926 5532 4096
Passcode: 555455
TITLE: An update on order-preserving Martin's Conjecture
ABSTRACT: Martin's Conjecture is a way of codifying a phenomenon observed
in computability theory: the only natural functions on the Turing degrees
seem to be the constant functions, the identity, and the transfinite
iterates of the Turing jump. While the full conjecture is wide open, there
has been significant progress on order-preserving Martin's
Conjecture--that is, Martin's Conjecture restricted to the functions which
preserve Turing-reducibility. In particular, the order-preserving version
has been settled positively for Borel functions whereas Martin's
Conjecture for even low-level Borel functions is open. In this talk, we'll
discuss a plan for pushing order-preserving Martin's Conjecture beyond
Borel functions involving some AD combinatorics, higher recursion theory,
and forcing. This is joint, in-progress work with Patrick Lutz.
Wednesday seminar
Prague Set Theory Seminar
4/1/2022 11:26:03
Dear all,
The seminar meets on Wednesday April 6th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: Jinřich Zapletal -- Pairs of generic extensions
I will present several natural variations of the notion of mutual
genericity for forcing extensions, show how to produce interesting
examples, and use them for consistency results in choiceless set theory.
Best,
David
(KGRC) Set Theory Research Seminar talk on Tuesday, April 5
Kurt Godel Research Center
4/1/2022 5:44:39
Set Theory Research Seminar
Kurt Gödel Research Center
Tuesday, April 5
"Fresh function spectra"
Wolfgang Wohofsky (KGRC)
My talk will be about the notion of fresh function and I will discuss the
corresponding spectrum. A function with domain lambda is fresh if it is
new but all its initial segments are in the ground model. I will give
general facts how to compute the fresh function spectrum, also discussing
what sets are realizable as a fresh function spectrum of a forcing.
Moreover, I will provide several examples, including well-known tree
forcings on omega such as Sacks, Laver, Miller, and Mathias forcing, as
well as Prikry and Namba forcing to illustrate the difference between
fresh functions and fresh subsets.
This is joint work with Vera Fischer and Marlene Koelbing.
Time and Place
Talk at 3:00pm in hybrid mode, in person as well as via Zoom.
Universität Wien
Institut für Mathematik
Kolingasse 14-16
1090 Wien
1st floor
Seminar room 10
Zoom: If you need the Zoom data and have not received the meeting link by
the day before the talk, please contact richard.springer@univie.ac.at!
(Please direct any other requests about the Set Theory Seminar and its
Zoom meeting to vera.fischer@univie.ac.at.)
Students at Uni Wien are strongly encouraged to attend the seminar in person.
Toronto Set Theory Seminar
Set Theory Seminar at the Fields Institute
3/28/2022 21:00:41
This Friday April 1, 13:30 (EDT, GMT -4)
Philipp Schlicht
will give a talk at the Toronto Set Theory Seminar @ The Fields
Institute
Title: Dichotomies for open directed hypergraphs on generalised Baire
spaces
Abstract: The open graph dichotomy for a subset X of the Baire space
states that any open graph on X either contains a large complete
subgraph or admits a countable colouring. It is a definable version of
the open colouring axiom for X and generalises the perfect set
property. Recently, this was generalised to infinite dimensions by
Miller, Carroy and Soukup. I will discuss extensions of this result to
generalised Baire spaces and a number of applications such as variants
of the Hurewicz dichotomy, the determinacy of Väänänen's game and the
asymmetric Baire property. This is a joint project with Dorottya
Sziraki.
Location: https://zoom.us/j/92701726800
Cross-Alps Logic Seminar (speaker: David Evans)
Cross-Alps Logic Seminar
3/28/2022 3:18:47
On Friday 01.04.2022 at 16:00
David Evans (Imperial College London)
will give a talk on
Amalgamation properties in measured structures
Please refer to the usual webpage of our
LogicGroup
for more details and the abstract of the talk.
The seminar will be held remotely through Webex. Please write to
luca.mottoros [at] unito [dot] itfor the link to the event.
The Cross-Alps Logic Seminar is co-organized by the logic groups
of Genoa, Lausanne, Turin and Udine as part of our collaboration
in the project PRIN 2017 'Mathematical logic: models, sets,
computability'.
This Week in Logic at CUNY
This Week in Logic at CUNY
3/27/2022 22:22:00
This Week in Logic at CUNY:
- - - - Monday, Mar 28, 2022 - - - -
Logic and Metaphysics Workshop
Date: Monday, March 28, 4.15-6.15 (NY time), GC 5382
For meeting information (including zoom link for those wishing to attend remotely), please sign up for our mailing list at
https://logic.commons.gc.cuny.edu/about/Dongwoo Kim (CUNY).
Title: Necessity, Essence and Explanation
Abstract: I shall discuss some of the relations between metaphysical modality, essence and explanation. The essentialist approach to metaphysical modality seeks to give an account of necessity (and thus of possibility) as having its source in essence. But what is essence, and in what sense and how does it give rise to necessity? In their recent paper “Essential Properties are Super-Explanatory: Taming Metaphysical Modality” (2020), Marion Godman, Antonella Mallozzi and David Papineau have attempted to address these issues with respect to aposteriori necessities concerning kinds. According to their account, the essence of a kind consists in the super-explanatory property—a single property that is causally responsible for a multitude of commonalities shared by the instances of the kind. And they argue that this super-explanatory notion of essence offers a principled account of aposteriori necessities concerning kinds. In this talk, I am going to argue that their account is not satisfactory. I shall examine two main arguments of GMP that the super-explanatory property of a kind is metaphysically necessary and argue that they both are fallacious. Along the way, a general problem will emerge that applies to any account that tries to explicate the notion of essence in terms of an explanatory relation.
- - - - Tuesday, Mar 29, 2022 - - - -
Models of Peano Arithmetic (MOPA)
Monday, March 29, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
Erez Shochat, St. Francis College
A Survey on the Automorphism Groups of Countable (Boundedly) Recursively Saturated Models of PA
In this talk we discuss important results concerning the automorphism groups of countable recursively saturated models of PA and automorphism groups of the countable boundedly recursively saturated models of PA which are short (aka short recursively saturated models). We compare and contrast and also list some open questions.
- - - - Wednesday, Mar 30, 2022 - - - -
The New York City Category Theory Seminar
Department of Computer Science
Department of Mathematics
The Graduate Center of The City University of New York
New URL:
http://www.sci.brooklyn.cuny.edu/~noson/Seminar/index.htmlContact N Yanofsky for zoom info (
noson@sci.brooklyn.cuny.edu)
Speaker: Morgan Rogers, Universit`a degli Studi dell’Insubria.
Date and Time: Wednesday March 30, 2022, 7:00 - 8:30 PM., on Zoom.
Title: Toposes of Topological Monoid Actions.
Abstract: Anyone encountering topos theory for the first time will be familiar with the fact that the category of actions of a monoid on sets is a special case of a presheaf topos. It turns out that if we equip the monoid with a topology and consider the subcategory of continuous actions, the result is still a Grothendieck topos. It is possible to characterize such toposes in terms of their points, and along the way extract canonical representing topological monoids, the complete monoids. I'll sketch the trajectory of this story, present some positive and negative results about Morita-equivalence of topological monoids, and explain how one can extract a semi-Galois theory from this set-up.
- - - - Thursday, Mar 31, 2022 - - - -
- - - - Friday, Apr 1, 2022 - - - -
Set Theory Seminar
CUNY Graduate Center, Friday, April 1, 12:30pm
The seminar will take place virtually at 12:30pm US Eastern Standard Time. Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
Vera Fischer, University of Vienna
Next Week in Logic at CUNY:
- - - - Monday, Apr 4, 2022 - - - -
Logic and Metaphysics WorkshopDate: Monday, April 4, 4.15-6.15 (NY time), GC 5382For meeting information (including zoom link for those wishing to attend remotely), please sign up for our mailing list at https://logic.commons.gc.cuny.edu/about/Jenn McDonald (Columbia)
Title: Causal Relativism
Abstract: In this talk, I defend a kind of causal relativism. I argue that actual causation cannot be taken to hold simpliciter between two particular things (‘things’ such as events, states-of-affairs, etc.). Instead, actual causation holds only relative to a background space of possibilities – a modal profile. The argument applies generally to any difference-making analysis of actual causation. But I will use the framework of structural equation models to make the case. I first demonstrate that structural equation models represent situations in this way – as relative to some modal profile or other. This observation is underappreciated in the literature. I show how it raises a problem for all extant analyses of actual causation in terms of these models. This problem is best responded to by a kind of causal relativism, or so I will argue. Notably, the problem cannot be avoided by rejecting a structural equation framework. While the framework is useful for its illustration, the problem arises for any analysis governed by the idea that a cause is what makes a difference in an effect’s occurrence.
Speaker: Jason Parker, Brandon University in Manitoba.
Date and Time: Wednesday April 6, 2022, 7:00 - 8:30 PM., on Zoom.
Title: Enriched structure-semantics adjunctions and monad-theory equivalences for subcategories of arities.
Abstract: Several structure-semantics adjunctions and monad-theory equivalences have been established in category theory. Lawvere (1963) developed a structure-semantics adjunction between Lawvere theories and tractable Set-valued functors, which was subsequently generalized by Linton (1969), while Dubuc (1970) established a structure-semantics adjunction between V-theories and tractable V-valued V-functors for a symmetric monoidal closed category V. It is also well known (and due to Linton) that there is an equivalence between Lawvere theories and finitary monads on Set. Generalizing this result, Lucyshyn-Wright (2016) established a monad-theory equivalence for eleutheric systems of arities in arbitrary closed categories. Building on earlier work by Nishizawa and Power, Bourke and Garner (2019) subsequently proved a general monad-theory equivalence for arbitrary small subcategories of arities in locally presentable enriched categories. However, neither of these equivalences generalizes the other, and there has not yet been a general treatment of enriched structure-semantics adjunctions that specializes to those established by Lawvere, Linton, and Dubuc.
Motivated by these considerations, we develop a general axiomatic framework for studying enriched structure-semantics adjunctions and monad-theory equivalences for subcategories of arities, which generalizes all of the aforementioned results and also provides substantial new examples of relevance for topology and differential geometry. For a subcategory of arities J in a V-category C over a symmetric monoidal closed category V, Linton’s notion of clone generalizes to provide enriched notions of J-theory and J-pretheory, which were also employed by Bourke and Garner (2019). We say that J is amenable if every J-theory admits free algebras, and is strongly amenable if every J-pretheory admits free algebras. If J is amenable, then we obtain an idempotent structure-semantics adjunction between certain J-pretheories and J-tractable V-categories over C, which yields an equivalence between J-theories and J-nervous V-monads on C. If J is strongly amenable, then we also obtain a rich theory of presentations for J-theories and J-nervous V-monads. We show that many previously studied subcategories of arities are (strongly) amenable, from which we recover the aforementioned structure-semantics adjunctions and monad-theory equivalences. We conclude with the result that any small subcategory of arities in a locally bounded closed category is strongly amenable, from which we obtain structure-semantics adjunctions and monad-theory equivalences in (e.g.) many convenient categories of spaces.
Joint work with Rory Lucyshyn-Wright.
- - - - Thursday, Apr 7, 2022 - - - -
- - - - Friday, Apr 8, 2022 - - - -
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to
jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email
jreitz@nylogic.org.
Kacper Kucharski, Using elementary submodels in topology
IMPAN Working Group in Applications of Set Theory
3/26/2022 12:10:18
Seminar: Working group in applications of set theory, IMPAN
Tuesday, 29.03.2022, at 13.15, room 403
Speaker: Kacper Kucharski, (MIM UW)
Title: Using elementary submodels in topology
Abstact: "The main goal of the talk is to present proofs of interesting topological theorems using elementary submodels. One theorem will be the classical Arhangel'skii's result which says that the cardinality of a compact Hausdorff first countable space is at most the continuum. The second part of the talk will be focused on presenting so-called reflection results e.g., Dow's theorem: every nonmetrizable compact Hausdorff space contains a nonmetrizable subspace of cardinality ω_1"
Visit our seminar page which may include some future talks at
https://www.impan.pl/~set_theory/Seminar/
Wednesday seminar
Prague Set Theory Seminar
3/25/2022 5:09:44
Dear all,
The seminar meets on Wednesday March 30th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: Ziemowit Kostana -- Games played with diamonds
Parametrized diamonds are combinatorial principles that imply many
consequences of the original Jensen's Diamond, yet are consistent with
the CH failing. Informally speaking, they are in similar relation to
Jensen's Diamond, as cardinal invariants of the Cichoń's diagram are to CH.
The modern framework for these axioms was described by Dzamonja, Hrusak,
and ... I would like to show that some equivalent, or
"almost-equivalent", axioms can be formulated in a completely different,
game-theoretic, language. This gives additional insight on how these
axioms affect the universe of sets.
Best,
David
Logic Seminar Wednesday 30 March 2022 16:00 hrs at NUS by Wu Liuzhen
NUS Logic Seminar
3/24/2022 19:30:22
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 30 March 2022, 16:00 hrs
Talk via Zoom:
https://nus-sg.zoom.us/j/83049258042?pwd=UWViaWNvTFUrdFdhOHJCdEVydnVkdz09
Meeting ID: 830 4925 8042
Passcode: 1729=x3+y3
Speaker: Wu Liuzhen
Title: Continuum function and strongly compact cardinal
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract: The continuum function is a key and long-studied object
inside set theory. We will survey the study on the behavior of
continuum function in presence of strongly compact cardinals. We will
also introduce some major research problems in this area. Finally, We
discuss our recent work on forcing continuum function of some special
pattern.
(KGRC) seminar talks Tuesday, March 29 and Thursday, March 31
Kurt Godel Research Center
3/24/2022 10:59:07
For the two most recent sessions in the Set Theory Research Seminar, video has
been recorded. So if you missed them or want to rewatch them, here they are:
Jeffrey Bergfalk, "A family of higher dimensional partition principles"
https://univienna.zoom.us/rec/share/iYgs9rLaHvrhRtdXzF4Swr31cGn0kZZchw0Qp_GBFWkV2h2P1k-NThPDZ2y43-GO.SQrJ2KqoAMvNPG91
Passcode vN70.uy1
Stefan Hoffelner, "Forcing the \Pi^1_n-uniformization property"
https://univienna.zoom.us/rec/share/4AI5rQ3rTJTGyOFwTZXvdCb2T3pPC4nBwBLuXZSFvctbA_b4U4wuuTt8sPKdYFwv.PehtSISZx_8QLZnE
Passcode Vkf%0@TD
* * *
Set Theory Research Seminar
Kurt G?del Research Center
Tuesday, March 29
"P-measures in the random forcing"
Damian Sobota (KGRC)
Let $\mu$ be a finitely additive probability measure on $\omega$ which
vanishes on points, that is, $\mu(\{n\})=0$ for every $n$. It follows
immediately that $\mu$ is not $\sigma$-additive, however it may be almost
$\sigma$-additive in the following weak sense. We say that $\mu$ is a
\textit{P-measure} if for every decreasing sequence $(A_n)$ of subsets of
$\omega$ there is a subset $A$ such that $A\setminus A_n$ is finite for
every $n$ and $\mu(A)=\lim_n \mu(A_n)$. It follows immediately that, e.g.,
an ultrafilter $\mathcal{U}$ on $\omega$ is a P-point if and only if the
one-point measure $\delta_\mathcal{U}$ is a P-measure. And similarly as in
the case of P-points the existence of P-measures is independent of ZFC.
During my talk I will discuss basic properties of P-measures and show, at
least briefly, that using old ideas of Solovay and Kunen one can obtain a
non-atomic P-measure in the random model. The latter result implies that
in this model there exists a nowhere dense ccc P-set in $\omega^*$, which
may be treated as a (weak) partial answer to the question asking whether
there are P-points in the random model.
This is a joint work with Piotr Borodulin-Nadzieja.
Time and Place
Talk at 3:00pm in hybrid mode, in person as well as via Zoom.
Universit?t Wien
Institut f?r Mathematik
Kolingasse 14-16
1090 Wien
1st floor
Seminar room 10
Zoom: If you need the Zoom data and have not received the meeting link by
the day before the talk, please contact richard.springer@univie.ac.at!
(Please direct any other requests about the Set Theory Seminar and its
Zoom meeting to vera.fischer@univie.ac.at.)
Students at Uni Wien are strongly encouraged to attend the seminar in person.
* * *
Logic Colloquium
Kurt G?del Research Center
Thursday, March 31
"Small uncountable objects in Banach space theory"
Damian Sobota (KGRC)
During my talk I will provide several examples presenting the impact which
the (non-)existence of miscellaneous uncountable combinatorial and
set-theoretic substructures of various basic spaces (such as the set
$P(\mathbb{N})$ of all subsets of the set $\mathbb{N}$ of natural numbers
or the set $\mathbb{N}^\mathbb{N}$ of all functions from $\mathbb{N}$ into
$\mathbb{N}$) has on structural and topological properties of Banach
spaces.
Time and Place
Talk at 3:00pm
Universit?t Wien
Institut f?r Mathematik
Lecture Hall HS 13
2nd floor
Oskar-Morgenstern-Platz 1
1090 Wien
Two seminars March 29: Ibarlucía (10AM) and Neeman (3:30PM)
Carnegie Mellon Logic Seminar
3/24/2022 6:07:30
TUESDAY, March 29, 2022
Set Theory Seminar: 10:30 A.M., Online, Tomás Ibarlucía, Université de
Paris
Please note the unusual time.
Join Zoom Meeting:
https://cmu.zoom.us/j/92655324096?pwd=VUhSSlkrdHMxbTlSYUMxYzFXM01kdz09
Meeting ID: 926 5532 4096
Passcode: 555455
TITLE: Approximate isomorphism of randomizations with a distinguished
small substructure
ABSTRACT: I will discuss a joint work with James Hanson in which we study
the relation of approximate isomorphism in a certain class of metric
structures---specifically, randomizations (in the sense of Ben
Yaacov--Keisler) of omega-categorical, omega-stable classical structures,
enriched with a predicate for a distinguished small elementary
substructure; "small" meaning that the pair consisting of the
randomization and its substructure forms a model of the theory of
beautiful pairs (in the sense of Poizat) of models of the randomized
theory. An approximate isomorphism between two such pairs is an
isomorphism of the randomizations that brings the distinguished elementary
substructures close in the Hausdorff metric.
We prove that for randomized infinite sets with no further structure, any
two pairs of this kind are approximately isomorphic (and that this extends
to other cases). On the other hand, we show that approximate isomorphism
fails for certain pairs of randomized vector spaces over finite sets (and,
in fact, for a much larger class of examples). These results provide both
a new positive instance and a refutation of a conjecture of Ben
Yaacov--Berenstein--Henson, which claimed that if T is an
omega-categorical, omega-stable metric theory, then the theory of
beautiful pairs of models of T should be approximately omega-categorical.
TUESDAY, March 29, 2022
Mathematical logic seminar: 3:30 P.M., Online, Itay Neeman, UCLA
Join Zoom Meeting:
https://cmu.zoom.us/j/92655324096?pwd=VUhSSlkrdHMxbTlSYUMxYzFXM01kdz09
Meeting ID: 926 5532 4096
Passcode: 555455
TITLE: Restrictions of OCA_T with large continuum
ABSTRACT: Todorcevic's Open Coloring Axiom (OCA_T) states that any open
graph on a separable metric space is either countably chromatic, or admits
an uncountable clique. OCA_T has many interesting and important
applications. Its known consistency proofs all lead to models where the
continuum is $\aleph_2$. It is therefore natural to ask whether it implies
that the continuum is $\aleph_2$, or whether there are other consistency
proofs leading to models with larger continuum. (OCA_T negates the CH.)
This question is still open. However we show that the restriction of OCA_T
to spaces of size less than the continuum is consistent with arbitrarily
large values of the continuum. Earlier work by Farah obtained this for the
restriction to spaces of size $\aleph_1$
Correction to previous subject line
Carnegie Mellon Logic Seminar
3/24/2022 6:18:21
Two seminars March 29: Ibarlucía (10:30AM) and Neeman (3:30PM)
Cross-Alps Logic Seminar (speaker: Omer Ben-Neria)
Cross-Alps Logic Seminar
3/21/2022 11:52:47
On Friday 25.03.2022 at 16:00
Omer Ben-Neria (The Hebrew University of Jerusalem)
will give a talk on
Mathias-type Criterion for the Magidor Iteration of Prikry
forcings
Please refer to the usual webpage of our
LogicGroup
for more details and the abstract of the talk.
The seminar will be held remotely through Webex. Please write to
luca.mottoros [at] unito [dot] itfor the link to the event.
The Cross-Alps Logic Seminar is co-organized by the logic groups of
Genoa, Lausanne, Turin and Udine as part of our collaboration in the
project PRIN 2017 'Mathematical logic: models, sets, computability'.
Logic Seminar at NUS on Wed 23 March 2022 at 16:00 hrs by Wu Guohua, NTU
NUS Logic Seminar
3/21/2022 10:21:28
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 23 March 2022, 16:00 hrs
Talk via Zoom:
https://nus-sg.zoom.us/j/83049258042?pwd=UWViaWNvTFUrdFdhOHJCdEVydnVkdz09
Meeting ID: 830 4925 8042
Passcode: 1729=x3+y3
Speaker: Wu Guohua
Title: Splittings and nonsplittings of computably enumerable sets
Abstract: In this talk, I will review some existing work on splittings of
c.e. sets, and then present an ongoing paper on nonsplitting,
a joint work with Downey. The main result is the following.
Theorem: There are c.e. sets A and B such that B is strictly
Turing reducible to A and for any c.e. sets U, V, if U and V form
a set-splitting of A, then one of them is Turing reducible to B.
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
This Week in Logic at CUNY
This Week in Logic at CUNY
3/20/2022 22:30:00
This Week in Logic at CUNY:
- - - - Monday, Mar 21, 2022 - - - -
Logic and Metaphysics Workshop
Date: Monday, March 21, 4.15-6.15 (NY time), GC 5382
For meeting information (including zoom link for those wishing to attend remotely), please sign up for our mailing list at
https://logic.commons.gc.cuny.edu/about/Noson Yanofsky (CUNY)
Title: Why Mathematics Works so Well
Abstract: A major question in philosophy of science involves the unreasonable effectiveness of mathematics in physics. Why should mathematics, created or discovered, with nothing empirical in mind be so perfectly suited to describe the laws of the physical universe? To answer this, we review the well-known fact that the defining properties of the laws of physics are their symmetries. We then show that there are similar symmetries of mathematical facts and that these symmetries are the defining properties of mathematics. By examining the symmetries of physics and mathematics, we show that the effectiveness is actually quite reasonable. In essence, we show that the regularities of physics are a subset of the regularities of mathematics.
- - - - Tuesday, Mar 22, 2022 - - - -
Models of Peano Arithmetic (MOPA)
Monday, March 22, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
Ermek Nurkhaidarov, Penn State Mont Alto
Generic Automorphisms
In this talk we investigate generic automorphisms of countable models. Hodges-Hodkinson-Lascar- Shelah 93 introduces the notion of SI (small index) generic automorphisms which are used to show the small index property. Truss 92 defines the notion of Truss generic automorphisms. We study the relationship between these two types of generic automorphisms.
Speaker: Joseph Dimos.
Date and Time: Wednesday March 23, 2022, 7:00 - 8:30 PM., on Zoom.
Title: Introduction to Fusion Categories and Some Applications.
Abstract: Tensor categories and multi-tensor categories have strong alignment with module categories. We can use the multi-tensor categories C in conjunction with classifying tensor algebras wrt C. From here, we can illustrate some examples of tensor categories: the category Vec of k-vector spaces that gives us a fusion category. This is defined as a category Rep(G) of some finite dimensional k-representations of a group G. From here, I will walk through the correspondence of tensor categories (Etingof) and fusion categories. Throughout, I will indicate a few unitary and non-unitary cases of fusion categories. Those unitary fusion categories are those that admit a uniquely monoidal structure. For example, this draws upon [Jones 1983] for finite index and finite depth that bridges a subfactor A-bimodule B to provide a full subcategory of some category A by its module structure. I will discuss some of these components throughout and explain the Morita equivalence of fusion categories.
- - - - Thursday, Mar 24, 2022 - - - -
- - - - Friday, Mar 25, 2022 - - - -
Set Theory Seminar
CUNY Graduate Center, Friday, March 25, 12:30pm
The seminar will take place virtually at 12:30pm US Eastern Standard Time. Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
Vera Fischer, University of Vienna
Next Week in Logic at CUNY:
- - - - Monday, Mar 28, 2022 - - - -
Logic and Metaphysics Workshop
Date: Monday, March 28, 4.15-6.15 (NY time), GC 5382
For meeting information (including zoom link for those wishing to attend remotely), please sign up for our mailing list at
https://logic.commons.gc.cuny.edu/about/Dongwoo Kim (CUNY).
Title: Necessity, Essence and Explanation
Abstract: I shall discuss some of the relations between metaphysical modality, essence and explanation. The essentialist approach to metaphysical modality seeks to give an account of necessity (and thus of possibility) as having its source in essence. But what is essence, and in what sense and how does it give rise to necessity? In their recent paper “Essential Properties are Super-Explanatory: Taming Metaphysical Modality” (2020), Marion Godman, Antonella Mallozzi and David Papineau have attempted to address these issues with respect to aposteriori necessities concerning kinds. According to their account, the essence of a kind consists in the super-explanatory property—a single property that is causally responsible for a multitude of commonalities shared by the instances of the kind. And they argue that this super-explanatory notion of essence offers a principled account of aposteriori necessities concerning kinds. In this talk, I am going to argue that their account is not satisfactory. I shall examine two main arguments of GMP that the super-explanatory property of a kind is metaphysically necessary and argue that they both are fallacious. Along the way, a general problem will emerge that applies to any account that tries to explicate the notion of essence in terms of an explanatory relation.
- - - - Tuesday, Mar 29, 2022 - - - -
Models of Peano Arithmetic (MOPA)
Monday, March 29, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
Erez Shochat, St. Francis College
- - - - Wednesday, Mar 30, 2022 - - - -
The New York City Category Theory Seminar
Department of Computer Science
Department of Mathematics
The Graduate Center of The City University of New York
New URL:
http://www.sci.brooklyn.cuny.edu/~noson/Seminar/index.htmlContact N Yanofsky for zoom info (
noson@sci.brooklyn.cuny.edu)
Speaker: Morgan Rogers, Universit`a degli Studi dell’Insubria.
Date and Time: Wednesday March 30, 2022, 7:00 - 8:30 PM., on Zoom.
Title: TBA.
- - - - Thursday, Mar 31, 2022 - - - -
- - - - Friday, Apr 1, 2022 - - - -
Set Theory Seminar
CUNY Graduate Center, Friday, April 1, 12:30pm
The seminar will take place virtually at 12:30pm US Eastern Standard Time. Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
Vera Fischer, University of Vienna
- - - - Other Logic News - - - -
- - - - Web Site - - - -
"Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)"
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to
jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email
jreitz@nylogic.org.
Kamil Ryduchowski, Elementary submodels and infinitary combinatorics
IMPAN Working Group in Applications of Set Theory
3/19/2022 9:27:34
Seminar: Working group in applications of set theory, IMPAN
Tuesday, 22.03.2022, at 13.15, room 403
Speaker: Kamil Ryduchowski, (MIM UW)
Title: Elementary submodels and infinitary combinatorics
Abstact: "We will present techniques of using elementary submodels as a tool in infinitary combinatorics. We shall show short, elegant proofs of, among others, the Delta-system lemma, the pressing-down lemma, Erdos-Dushnik-Miller theorem."
Visit our seminar page which may include some future talks at
https://www.impan.pl/~set_theory/Seminar/
(KGRC) Set Theory Research Seminar talk on Tuesday, March 22
Kurt Godel Research Center
3/17/2022 11:00:15
Set Theory Research Seminar
Kurt G?del Research Center
Tuesday, March 22
"A family of higher dimensional partition principles"
Jeffrey Bergfalk (KGRC)
This talk will be an exposition of the recent work \emph{A descriptive approach
to higher derived limits}, joint with Nathaniel Bannister, Justin Moore, and
Stevo Todorcevic (arXiv:2203.00165). The material of this paper is somewhat
more ranging than its title would suggest.
At its heart is a new family of partition principles which synthesize several
recent advances in the study of higher derived limits, rendering those results
far more amenable to combinatorial analyses.
These principles admit formulation on any directed quasi-order, and are of
particular, and interrelated, interest on the quasi-orders
$({^\omega}\omega,\leq^*)$ and the ordinals $\omega_n$. A main implication of
these principles in any case is the triviality of (higher dimensionally)
coherent families of functions; we'll use any remaining time to note ways that
such objects, and even higher derived limits, are closer to classical set
theoretic concerns than perhaps tends to be realized.
Time and Place
Talk at 3:00pm in hybrid mode, in person as well as via Zoom.
Universit?t Wien
Institut f?r Mathematik
Kolingasse 14-16
1090 Wien
1st floor
Seminar room 10
Zoom: If you need the Zoom data and have not received the meeting link by
the day before the talk, please contact richard.springer@univie.ac.at!
(Please direct any other requests pertaining to the Set Theory Seminar and
its Zoom meeting to vera.fischer@univie.ac.at.)
Students at Uni Wien are strongly encouraged to attend the seminar in person.
Wednesday seminar
Prague Set Theory Seminar
3/17/2022 8:19:30
Dear all,
The seminar meets on Wednesday March 23rd at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: Sam Braunfeld -- Monadic dividing lines and hereditary classes
We will discuss how monadic versions of dividing lines in model theory
(NIP, stability, NFCP) can be used to prove structure and non-structure
results in hereditary classes, which can in turn be used for
combinatorial applications.
Best,
David
Logic seminar Tuesday March 22
Carnegie Mellon Logic Seminar
3/16/2022 12:18:51
TUESDAY, March 22, 2022
Mathematical logic seminar: 3:30 P.M., Online, Colin Jahel, Carnegie
Mellon University
Join Zoom Meeting:
https://cmu.zoom.us/j/92655324096?pwd=VUhSSlkrdHMxbTlSYUMxYzFXM01kdz09
Meeting ID: 926 5532 4096
Passcode: 555455
TITLE: Asymptotic theories and homomorphically-avoided structures
ABSTRACT: Given a class of finite structures, one can consider μn the
uniform measure on structures in said class of size n. We study the
asymptotic behavior, when n goes to infinity, of the family (μn)n. In
particular, one can ask: which sentences have converging probability, and
when is this limit non-zero? I will present our results for classes of
graphs and digraphs, in particular classes not containing any homorphic
copies of certain sets of finite structures. Joint work with Manuel
Bodirsky.
Logic Seminar 16 March 2022 16:00 hrs SGT by Leszek Kolodziejcyk, University of Warsaw
NUS Logic Seminar
3/15/2022 21:38:58
Hello, there were various typing errors in the announcement of today's talk
including an error of the timing in the email subject. Therefore I resend the
announcement. Best regards, Frank
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 16 March 2022, 16:00 hrs
Talk via Zoom:
https://nus-sg.zoom.us/j/83049258042?pwd=UWViaWNvTFUrdFdhOHJCdEVydnVkdz09
Meeting ID: 830 4925 8042
Passcode: 1729=x3+y3
Speaker: Leszek Kolodziejczyk
Title: A conservativity result for not-WO(omega^omega)
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract:
The Chong-Slaman-Yang construction of a model of RT^2_2 not satisfying
Sigma^0_2-induction makes crucial use of a principle known as BME_1. This
principle was later shown by Kreuzer and Yokoyama to be equivalent to
WO(omega^omega), the statement that omega^omega is well-ordered.
I will talk about the following result: if A is any set in a model of RCA_0
+ Sigma^0_2-collection such that Sigma_2(A)-induction fails, then there is
a descending sequence in omega^omega that is low in A. As a consequence,
the negation of WO(omega^omega) is Pi11-conservative over RCA_0 +
BSigma^0_2 + not-ISigma^0_2.
This result has some potentially interesting corollaries:
- If RCA_0 + RT^2_2 is Pi^1_1-conservative over BSigma^0_2, then this can
be proved by considering only models in which BME_1 fails.
- The formula "X is a well-order" is not provably equivalent to any
Sigma^1_1 formula over COH + BSigma^0_2 + not-ISigma^0_2. (In contrast, by
earlier work of Fiori Carones, Wong, Yokoyama, and myself, the theory
WKL*_0 + not-ISigma^0_1, which is to some extent analogous to COH +
BSigma^0_2 + not-ISigma^0_2, proves a collapse of the analytic hierarchy to
Delta^1_1.)
- There exist two models of RCA_0 + COH + BSigma^0_2 that share a
first-order universe and a common counterexample to ISigma^0_2 but are not
elementarily equivalent. (In contrast, by the work of Fiori Carones et al.
mentioned above, the families of Delta^0_2-definable sets of any such two
models have to be elementarily equivalent.)
The conservativity result is a side product of a larger project joint with
Fiori Carones, Yokoyama, and others.
Gruesse aus Singapur
NUS Logic Seminar
3/15/2022 21:40:13
Hello, there were various typing errors in the announcement of today's talk
including an error of the timing in the email subject. Therefore I resend the
announcement. Best regards, Frank
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 16 March 2022, 16:00 hrs
Talk via Zoom:
https://nus-sg.zoom.us/j/83049258042?pwd=UWViaWNvTFUrdFdhOHJCdEVydnVkdz09
Meeting ID: 830 4925 8042
Passcode: 1729=x3+y3
Speaker: Leszek Kolodziejczyk
Title: A conservativity result for not-WO(omega^omega)
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract:
The Chong-Slaman-Yang construction of a model of RT^2_2 not satisfying
Sigma^0_2-induction makes crucial use of a principle known as BME_1. This
principle was later shown by Kreuzer and Yokoyama to be equivalent to
WO(omega^omega), the statement that omega^omega is well-ordered.
I will talk about the following result: if A is any set in a model of RCA_0
+ Sigma^0_2-collection such that Sigma_2(A)-induction fails, then there is
a descending sequence in omega^omega that is low in A. As a consequence,
the negation of WO(omega^omega) is Pi11-conservative over RCA_0 +
BSigma^0_2 + not-ISigma^0_2.
This result has some potentially interesting corollaries:
- If RCA_0 + RT^2_2 is Pi^1_1-conservative over BSigma^0_2, then this can
be proved by considering only models in which BME_1 fails.
- The formula "X is a well-order" is not provably equivalent to any
Sigma^1_1 formula over COH + BSigma^0_2 + not-ISigma^0_2. (In contrast, by
earlier work of Fiori Carones, Wong, Yokoyama, and myself, the theory
WKL*_0 + not-ISigma^0_1, which is to some extent analogous to COH +
BSigma^0_2 + not-ISigma^0_2, proves a collapse of the analytic hierarchy to
Delta^1_1.)
- There exist two models of RCA_0 + COH + BSigma^0_2 that share a
first-order universe and a common counterexample to ISigma^0_2 but are not
elementarily equivalent. (In contrast, by the work of Fiori Carones et al.
mentioned above, the families of Delta^0_2-definable sets of any such two
models have to be elementarily equivalent.)
The conservativity result is a side product of a larger project joint with
Fiori Carones, Yokoyama, and others.
Cross-Alps Logic Seminar (speaker: Damir Dzhafarov)
Cross-Alps Logic Seminar
3/14/2022 18:12:16
On Friday 18.03.2022 at 16:00
Damir Dzhafarov (University of Connecticut)
will give a talk on
The SRT22 vs. COH problem
Please refer to the usual webpage of our
LogicGroup
for more details and the abstract of the talk.
The seminar will be held remotely through Webex. Please write to
luca.mottoros [at] unito [dot] itfor the link to the event.
The Cross-Alps Logic Seminar is co-organized by the logic groups of
Genoa, Lausanne, Turin and Udine as part of our collaboration in the
project PRIN 2017 'Mathematical logic: models, sets, computability'.
This Week in Logic at CUNY
This Week in Logic at CUNY
3/13/2022 22:56:00
This Week in Logic at CUNY:
- - - - Monday, Mar 14, 2022 - - - -
Logic and Metaphysics Workshop
Date: Monday, March 14, 4.15-6.15 (NY time), GC 5382
For meeting information (including zoom link for those wishing to attend remotely), please sign up for our mailing list at
https://logic.commons.gc.cuny.edu/about/Wilfrid Hodges (King’s)
Title: Avicenna motivates two new logics
Abstract: The logician Avicenna (Ibn Sina in Arabic) tells us that some thousand and twenty years ago he discovered a group of previously unknown logics. He seems to have been the first logician – at least west of India and after the ancient Greeks – who made any such claim. We will examine two of these new logics and his motivations for them. The first new logic, discovered in around 994 when Avicenna was about eighteen years old, was rediscovered by Boole in the mid 19th century. We will study some features of it that were important to Avicenna (and to some recent logicians) but apparently missed by Boole. The second new logic, probably from around 1000, seems to be the earliest logic with inference rules that act below the surface levels of the formulas. It was impossible to state the inference rules correctly before Frege introduced the notion of scope, but we will see how far Avicenna got.
- - - - Tuesday, Mar 15, 2022 - - - -
Models of Peano Arithmetic (MOPA)
Monday, March 15, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
Thomas Ferguson, University of Amsterdam and University of St. Andrews
Models of Relevant Arithmetic
In the 1970s, the logician and philosopher Robert Meyer proposed a novel response to Goedel's Incompleteness Theorems, suggesting that perhaps the results' impact could be blunted by analyzing Peano arithmetic with a weaker deductive system. Initial successes of the program of relevant arithmetic were positive. E.g., R# (the theory of Peano arithmetic under the relevant logic R) can be shown consistent in the sense of not proving 0=1 and this can be shown through arguably finitistic methods. In this talk I will discuss the rise and fall of Meyer's program, detailing the philosophical foundations, its positive development, and the context of Harvey Friedman's negative result in 1992. I'll also suggest why the program, although not necessarily successful, is nevertheless an interesting object of study.
Also note that a great deal of context—including Meyer's two long-unpublished monographs on the topic—have recently appeared in a special issue of the Australasian Journal of Logic I co-edited with Graham Priest, which can be found at https://ojs.victoria.ac.nz/ajl/issue/view/751.
- - - - Wednesday, Mar 16, 2022 - - - -
The New York City Category Theory Seminar
Department of Computer Science
Department of Mathematics
The Graduate Center of The City University of New York
New URL:
http://www.sci.brooklyn.cuny.edu/~noson/Seminar/index.htmlContact N Yanofsky for zoom info (
noson@sci.brooklyn.cuny.edu)
Speaker: Jin-Cheng Guu, Stony Brook University.
Date and Time: Wednesday March 16, 2022, 7:00 - 8:30 PM., on Zoom.
Title: Topological Quantum Field Theories from Monoidal Categories.
Abstract: We will introduce the notion of a topological quantum field theory (tqft) and a monoidal category. We will then construct a few (extended) tqfts from monoidal categories, and show how quantum invariants of knots and 3-manifolds were obtained. If time permits, I will discuss (higher) values in (higher) codimensions based on my recent work on categorical center of higher genera (joint with A. Kirillov and Y. H. Tham).
- - - - Thursday, Mar 17, 2022 - - - -
- - - - Friday, Mar 18, 2022 - - - -
Next Week in Logic at CUNY:
- - - - Monday, Mar 21, 2022 - - - -
Logic and Metaphysics Workshop
Date: Monday, March 21, 4.15-6.15 (NY time), GC 5382
For meeting information (including zoom link for those wishing to attend remotely), please sign up for our mailing list at
https://logic.commons.gc.cuny.edu/about/Noson Yanofsky (CUNY)
Title: Why Mathematics Works so Well
Abstract: A major question in philosophy of science involves the unreasonable effectiveness of mathematics in physics. Why should mathematics, created or discovered, with nothing empirical in mind be so perfectly suited to describe the laws of the physical universe? To answer this, we review the well-known fact that the defining properties of the laws of physics are their symmetries. We then show that there are similar symmetries of mathematical facts and that these symmetries are the defining properties of mathematics. By examining the symmetries of physics and mathematics, we show that the effectiveness is actually quite reasonable. In essence, we show that the regularities of physics are a subset of the regularities of mathematics.
- - - - Tuesday, Mar 22, 2022 - - - -
Models of Peano Arithmetic (MOPA)
Monday, March 22, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
Ermek Nurkhaidarov, Penn State Mont Alto
Speaker: Joseph Dimos.
Date and Time: Wednesday March 23, 2022, 7:00 - 8:30 PM., on Zoom.
Title: Introduction to Fusion Categories and Some Applications.
Abstract: Tensor categories and multi-tensor categories have strong alignment with module categories. We can use the multi-tensor categories C in conjunction with classifying tensor algebras wrt C. From here, we can illustrate some examples of tensor categories: the category Vec of k-vector spaces that gives us a fusion category. This is defined as a category Rep(G) of some finite dimensional k-representations of a group G. From here, I will walk through the correspondence of tensor categories (Etingof) and fusion categories. Throughout, I will indicate a few unitary and non-unitary cases of fusion categories. Those unitary fusion categories are those that admit a uniquely monoidal structure. For example, this draws upon [Jones 1983] for finite index and finite depth that bridges a subfactor A-bimodule B to provide a full subcategory of some category A by its module structure. I will discuss some of these components throughout and explain the Morita equivalence of fusion categories.
- - - - Thursday, Mar 24, 2022 - - - -
- - - - Friday, Mar 25, 2022 - - - -
Set Theory Seminar
CUNY Graduate Center, Friday, March 25, 12:30pm
The seminar will take place virtually at 12:30pm US Eastern Standard Time. Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
Vera Fischer, University of Vienna
- - - - Other Logic News - - - -
- - - - Web Site - - - -
"Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)"
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Jakub Andruszkiewicz, The club principle and its connections to the diamond principle
IMPAN Working Group in Applications of Set Theory
3/13/2022 4:08:38
Seminar: Working group in applications of set theory, IMPAN
Tuesday, 15.03.2022, at 13.15, room 403
Speaker: Jakub Andruszkiewicz, (UW/IM PAN)
Title: The club principle and its connections to the diamond principle
Abstact: The club principle was first introduced by Ostaszewski as a weakening of the diamond principle, as it plays a crucial role in his original construction of the Ostaszewski space. It is well-known that under CH those principles are equivalent and we will present a proof of this fact. We will also show by using an appropriate forcing extension that, as proven by Shelah, assuming CH is essential, i.e. it is consistent relative to ZFC that the club principle holds while the diamond principle does not.
Visit our seminar page which may include some future talks at
https://www.impan.pl/~set_theory/Seminar/
(KGRC) seminar talks Tuesday, March 15 and Thursday, March 17
Kurt Godel Research Center
3/11/2022 15:20:12
Set Theory Research Seminar
Kurt G?del Research Center
Tuesday, March 15
"Forcing the \Pi^1_n-uniformization property"
Stefan Hoffelner
(University of M?nster, Germany)
The uniformization property, introduced by N. Lusin in 1930, is an extensively
studied notion in descriptive set theory. For a given projective pointclass
$\Gamma$ it says that every subset of the plane which belongs to $\Gamma$ has a
uniformizing function whose graph is an element of $\Gamma$ as well. The
celebrated results of Y. Moschovakis on the one hand and D. Martin, J. Steel
and H. Woodin on the other, yield a natural and global description of the
behaviour of the uniformization property for projective pointclasses under the
assumption of large cardinals. In particular, under PD, for every natural
number n, $\Pi^1_{2n+1}$-sets and hence $\Sigma^1_{2n+2}$-sets do have the
uniformization property.
Yet the question of universes which display an alternative behaviour of theses
regularity properties has remained in large parts a complete mystery, mostly
due to the absence of forcing techniques to produce such models.
Consequentially, a lot of very natural problems have remained wide open ever
since.
In my talk, I want to outline some recently obtained tools, which turn the
question of forcing a universe with the $\Pi^1_n$-uniformization property into
a fixed point problem for certain sets of forcing notions. This fixed point
problem can be solved, yielding a specific set of forcing notions which in turn
can be used to force the Uniformization property (for n>2) over fine structural
inner models with large cardinals (for n=3, the inner model is just L). For
even n, these universes witness for the first time the consistency (relative to
the existence of n-3 many Woodin cardinals) of the $\Pi^1_{n}$-uniformization
property, and, for odd n, give new lower bounds in terms of consistency
strength.
Time and Place
Talk at 3:00pm in hybrid mode, in person as well as via Zoom.
Universit?t Wien
Institut f?r Mathematik
Kolingasse 14-16
1090 Wien
1st floor
Seminar room 10
Zoom: If you need the Zoom data and have not received the meeting link by
the day before the talk, please contact richard.springer@univie.ac.at!
(Please direct any other requests pertaining to the Set Theory Seminar and
its Zoom meeting to vera.fischer@univie.ac.at.)
Students at Uni Wien are strongly encouraged to attend the seminar in person.
* * *
Logic Colloquium
Kurt G?del Research Center
Thursday, March 17
"Forcing and the Separation, the Reduction and the Uniformization Property"
Stefan Hoffelner
(University of M?nster, Germany)
The Separation property, the Reduction property and the Uniformization
property, introduced in the 1920's and 1930's are three classical regularity
properties of pointclasses of the reals.
The celebrated results of Y. Moschovakis on the one hand and D. Martin, J.
Steel and H. Woodin on the other, yield a global description of the behaviour
of these regularity properties for projective pointclasses under the assumption
of large cardinals. These results, impressive as they are, still leave open a
lot of natural questions. To name a few we mention:
Do we need large cardinals to obtain their effects on the behaviour of these
regularity property?
Is the $\Sigma^1_{2n+1}$-separation property actually consistent for n >1? More
generally: to what extent can we produce set theoretic universes which display
a different behaviour of these regularity properties?
Are the separation the reduction and the uniformization property different
notions at all?
The goal of this talk to introduce the three mentioned regularity properties,
present a couple of these natural problems and discuss new results, utilising a
novel forcing technique, which answer some of them.
Time and Place
Talk at 3:00pm
Universit?t Wien
Institut f?r Mathematik
Lecture Hall HS 13
2nd floor
Oskar-Morgenstern-Platz 1
1090 Wien
Wednesday seminar
Prague Set Theory Seminar
3/11/2022 3:53:59
Dear all,
The seminar meets on Wednesday March 16th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: David Uhrik -- The effect of MA on graphs on omega_1
I'll talk about Todorcevic's result that MA_omega1 implies that every
graph on omega_1 without an uncountable independent set contains a
clique of ordertype omega^2.
Best,
David
Logic Seminar 16 March 2022 17:00 hrs at NUS by Leszek Kolodziejczyk
NUS Logic Seminar
3/10/2022 3:42:14
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 16 March 2022, 16:00 hrs
Talk via Zoom:
https://nus-sg.zoom.us/j/83049258042?pwd=UWViaWNvTFUrdFdhOHJCdEVydnVkdz09
Meeting ID: 830 4925 8042
Passcode: 1729=x3+y3
Speaker: Leszek Kolodziejczyk
Title: A conservativity result for not-WO(omega^omega)
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract:
The Chong-Slaman-Young construction of a model of RT^2_2 not satisfying
Sigma^0_2-induction makes crucial use of a principle known as BME_1. This
principle was later shown by Kreuzer and Yokoyama to be equivalent to
WO(omega^omega), the statement that omega^omega is well-ordered.
I will talk about the following result: if A is any set in a model of RCA_0
+ Sigma^0_2-collection such that Sigma_2(A)-induction fails, then there is
a descending sequence in omega^omega that is low in A. As a consequence,
the negation of WO(omega^omega) is Pi11-conservative over RCA_0 +
BSigma^0_2 + not-ISigma^0_2.
This result has some potentially interesting corollaries:
- If RCA_0 + RT^2_2 is Pi^1_1-conservative over BSigma^0_2, then this can
be proved by considering only models in which BME_1 fails.
- The formula "X is a well-order" is not provably equivalent to any
Sigma^1_1 formula over COH + BSigma^0_2 + not-ISigma^0_2. (In contrast, by
earlier work of Fiori Carones, Wong, Yokoyama, and myself, the theory
WKL*_0 + not-ISigma^0_1, which is to some extent analogous to COH +
BSigma^0_2 + not-ISigma^0_2, proves a collapse of the analytic hierarchy to
Delta^1_1.)
- There exist two models of RCA_0 + COH + BSigma^0_2 that share a
first-order universe and a common counterexample to ISigma^0_2 but are not
elementarily equivalent. (In contrast, by the work of Fiori Carones et al.
mentioned above, the families of Delta^0_2-definable sets of any such two
models have to be elementarily equivalent.)
The conservativity result is a side product of a larger project joint with
Fiori Carones, Yokoyama, and others.
Logic Seminar 16 March 2022 17:00 hrs at NUS by Leszek Kolodziejczyk
NUS Logic Seminar
3/10/2022 3:41:24
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 16 March 2022, 16:00 hrs
Talk via Zoom:
https://nus-sg.zoom.us/j/83049258042?pwd=UWViaWNvTFUrdFdhOHJCdEVydnVkdz09
Meeting ID: 830 4925 8042
Passcode: 1729=x3+y3
Speaker: Leszek Kolodziejczyk
Title: A conservativity result for not-WO(omega^omega)
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract:
The Chong-Slaman-Young construction of a model of RT^2_2 not satisfying
Sigma^0_2-induction makes crucial use of a principle known as BME_1. This
principle was later shown by Kreuzer and Yokoyama to be equivalent to
WO(omega^omega), the statement that omega^omega is well-ordered.
I will talk about the following result: if A is any set in a model of RCA_0
+ Sigma^0_2-collection such that Sigma_2(A)-induction fails, then there is
a descending sequence in omega^omega that is low in A. As a consequence,
the negation of WO(omega^omega) is Pi11-conservative over RCA_0 +
BSigma^0_2 + not-ISigma^0_2.
This result has some potentially interesting corollaries:
- If RCA_0 + RT^2_2 is Pi^1_1-conservative over BSigma^0_2, then this can
be proved by considering only models in which BME_1 fails.
- The formula "X is a well-order" is not provably equivalent to any
Sigma^1_1 formula over COH + BSigma^0_2 + not-ISigma^0_2. (In contrast, by
earlier work of Fiori Carones, Wong, Yokoyama, and myself, the theory
WKL*_0 + not-ISigma^0_1, which is to some extent analogous to COH +
BSigma^0_2 + not-ISigma^0_2, proves a collapse of the analytic hierarchy to
Delta^1_1.)
- There exist two models of RCA_0 + COH + BSigma^0_2 that share a
first-order universe and a common counterexample to ISigma^0_2 but are not
elementarily equivalent. (In contrast, by the work of Fiori Carones et al.
mentioned above, the families of Delta^0_2-definable sets of any such two
models have to be elementarily equivalent.)
The conservativity result is a side product of a larger project joint with
Fiori Carones, Yokoyama, and others.
Cross-Alps Logic Seminar (speaker: Alessandro Andretta)
Cross-Alps Logic Seminar
3/7/2022 1:55:22
On Friday 11.03.2022 at 16:00
Alessandro Andretta (University of Turin)
will give a talk on
Sierpinski’s partitions with Sigma^1_2 pieces
Please refer to the usual webpage of our
LogicGroup
for more details and the abstract of the talk.
The seminar will be held remotely through Webex. Please write to
luca.mottoros [at] unito [dot] it for the link to the event.
The Cross-Alps Logic Seminar is co-organized by the logic groups of
Genoa, Lausanne, Turin and Udine as part of our collaboration in the
project PRIN 2017 'Mathematical logic: models, sets, computability'.
This Week in Logic at CUNY
This Week in Logic at CUNY
3/6/2022 22:30:00
This Week in Logic at CUNY:
- - - - Monday, Mar 7, 2022 - - - -
Logic and Metaphysics Workshop
Date: Monday, March 7, 4.15-6.15 (NY time), GC 5382
For meeting information (including zoom link for those wishing to attend remotely), please sign up for our mailing list at
https://logic.commons.gc.cuny.edu/about/David Papineau (King’s).
Title: Understanding Causal Inference
Abstract: The current pandemic has focused attention on the techniques used by epidemiologists and other non-experimental scientists to infer causal hypotheses from correlational data. These techniques, which hinge on assumptions about the way causal connections manifest themselves in conditional and unconditional correlations, pose an obvious philosophical challenge. What is it about causation that allows them to work? None of the mainstream accounts of causation—counterfactual, process, dispositional, regularity—casts any light on this question. Probabilistic and interventionist theories of causation do offer a direct response to the challenge, by positing a constitutive connection between causes and correlations, but I shall argue that these theories do not dig deep enough. Instead I shall develop an older idea—which goes back to H.A. Simon in the 1950s—that relates causal relationships to systems of structural equations with probabilistically independent exogenous variables. The attraction of this structural equations approach is that it allows us to view the correlational patterns as fallible evidence for causal relationships, rather than constitutive of them. I shall consider whether this approach can lead to a full reduction of causation and how it might accommodate quantum mechanical unpredictability.
- - - - Tuesday, Mar 8, 2022 - - - -
- - - - Wednesday, Mar 9, 2022 - - - -
- - - - Thursday, Mar 10, 2022 - - - -
- - - - Friday, Mar 11, 2022 - - - -
Set Theory Seminar
CUNY Graduate Center, Friday, March 11, 12:30pm
The seminar will take place virtually at 12:30pm US Eastern Standard Time. Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
William Chan, Carnegie Mellon University
Logic Workshop
CUNY Graduate Center, Friday, March 11, 2pm
The seminar will take place at the CUNY Graduate Center at 2pm in Room TBA.
Joel David Hamkins, Notre Dame University
Infinite wordle and the mastermind numbers
I shall introduce and consider the natural infinitary variations of Wordle, Absurdle, and Mastermind. Infinite Wordle extends the familiar finite game to infinite words and transfinite play—the code-breaker aims to discover a hidden codeword selected from a dictionary Δ⊆Σω of infinite words over a countable alphabet Σ by making a sequence of successive guesswords, receiving feedback after each guess concerning its accuracy. For any dictionary using the usual 26-letter alphabet, for example, the code-breaker can win in at most 26 guesses, and more generally in n guesses for alphabets of finite size n. Meanwhile, for some dictionaries on an infinite alphabet, infinite play is required, but the code-breaker can always win by stage ω on a countable alphabet, for any fixed dictionary. Infinite Mastermind, in contrast, is a subtler game than Wordle because only the number and not the position of correct bits is given. When duplication of colors is allowed, nevertheless, then the code-breaker can still always win by stage ω, but in the no-duplication variation, no countable number of guesses (even transfinite) is sufficient for the code-breaker to win. I therefore introduce the mastermind number, denoted mm, to be the size of the smallest winning no-duplication Mastermind guessing set, a new cardinal characteristic of the continuum, which I prove is bounded below by the additivity number add(M) of the meager ideal and bounded above by the covering number cov(M). In particular, the precise value of the mastermind number is independent of ZFC and can consistently be strictly between ℵ1 and the continuum 2ℵ0. In simplified Mastermind, where the feedback given at each stage includes only the numbers of correct and incorrect bits (omitting information about rearrangements), then the corresponding simplified mastermind number is exactly the eventually different number d(≠∗). http://jdh.hamkins.org/infinite-wordle-and-the-mastermind-numbers-cuny-logic-workshop-march-2022/
Next Week in Logic at CUNY:
- - - - Monday, Mar 14, 2022 - - - -
Logic and Metaphysics Workshop
Date: Monday, March 14, 4.15-6.15 (NY time), GC 5382
For meeting information (including zoom link for those wishing to attend remotely), please sign up for our mailing list at
https://logic.commons.gc.cuny.edu/about/Wilfrid Hodges (King’s)
Title: Avicenna motivates two new logics
Abstract: The logician Avicenna (Ibn Sina in Arabic) tells us that some thousand and twenty years ago he discovered a group of previously unknown logics. He seems to have been the first logician – at least west of India and after the ancient Greeks – who made any such claim. We will examine two of these new logics and his motivations for them. The first new logic, discovered in around 994 when Avicenna was about eighteen years old, was rediscovered by Boole in the mid 19th century. We will study some features of it that were important to Avicenna (and to some recent logicians) but apparently missed by Boole. The second new logic, probably from around 1000, seems to be the earliest logic with inference rules that act below the surface levels of the formulas. It was impossible to state the inference rules correctly before Frege introduced the notion of scope, but we will see how far Avicenna got.
- - - - Tuesday, Mar 15, 2022 - - - -
Models of Peano Arithmetic (MOPA)
Monday, March 15, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
Models of Relevant Arithmetic
Thomas Ferguson University of Amsterdam and University of St. Andrews
- - - - Wednesday, Mar 16, 2022 - - - -
The New York City Category Theory Seminar
Department of Computer Science
Department of Mathematics
The Graduate Center of The City University of New York
New URL:
http://www.sci.brooklyn.cuny.edu/~noson/Seminar/index.htmlContact N Yanofsky for zoom info (
noson@sci.brooklyn.cuny.edu)
Speaker: Jin-Cheng Guu, Stony Brook University.
Date and Time: Wednesday March 16, 2022, 7:00 - 8:30 PM., on Zoom.
Title: Topological Quantum Field Theories from Monoidal Categories.
Abstract: We will introduce the notion of a topological quantum field theory (tqft) and a monoidal category. We will then construct a few (extended) tqfts from monoidal categories, and show how quantum invariants of knots and 3-manifolds were obtained. If time permits, I will discuss (higher) values in (higher) codimensions based on my recent work on categorical center of higher genera (joint with A. Kirillov and Y. H. Tham).
- - - - Thursday, Mar 17, 2022 - - - -
- - - - Friday, Mar 18, 2022 - - - -
Set Theory Seminar
CUNY Graduate Center, Friday, March 18, 12:30pm
The seminar will take place virtually at 12:30pm US Eastern Standard Time. Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
William Chan, Carnegie Mellon University
- - - - Other Logic News - - - -
- - - - Web Site - - - -
"Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)"
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CMU math logic seminar on Tuesday, March 15
Carnegie Mellon Logic Seminar
3/5/2022 20:20:46
TUESDAY, March 15, 2022
Mathematical logic seminar: 3:30 P.M., Online, Alex Kruckman, Wesleyan
University
Join Zoom Meeting:
https://cmu.zoom.us/j/92655324096?pwd=VUhSSlkrdHMxbTlSYUMxYzFXM01kdz09
Meeting ID: 926 5532 4096
Passcode: 555455
TITLE: Properly ergodic structures
ABSTRACT: One natural notion of "random (countably infinite) L-structure"
is a probability measure on the space of L-structures with domain omega
which is invariant and ergodic for the natural action of the symmetric
group Sym(omega) on this space. We call such a measure an ergodic
structure. The most famous example of an ergodic structure is the
Erdős–Rényi random graph model on domain omega, which gives measure 1 to
the isomorphism type of the Rado graph. Ergodic structures also arise
naturally as limits of sequences of finite structures which are convergent
in the appropriate sense, generalizing the graph limits of Lovász and
Szegedy.
Some ergodic structures (like the Erdős–Rényi random graph model) are
almost surely isomorphic to a single countable structure (like the Rado
graph), and the countable structures which arise in this way have been
completely characterized by Ackerman, Freer, and Patel. In this talk, we
will consider properly ergodic structures, those which do not give measure
1 to any single isomorphism type. What do properly ergodic models "look
like"? To address this question, we develop an analogue of the Scott rank
for ergodic structures, which leads to a precise characterization of those
first-order theories (and, more generally, those sentences of the
infinitary logic L_{omega_1,omega}) which admit properly ergodic models.
This is joint work with Ackerman, Freer, and Patel.
Wednesday seminar
Prague Set Theory Seminar
3/4/2022 7:20:53
Dear all,
The seminar meets on Wednesday March 9th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program:
Chris Lambie-Hanson -- Higher-dimensional coherent Aronszajn trees
We will introduce a family of higher-dimensional analogues of coherent
Aronszajn trees arising from a cohomological analysis of ordinals,
considered as topological spaces with the order topology. We will
investigate the influence of large cardinals on the existence of such
higher-dimensional coherent Aronszajn trees and will prove that, if V=L,
then these higher-dimensional coherent Aronszajn trees exist everywhere
except where ruled out for trivial reasons. We will also present some
interesting open questions. This is joint work with Jeffrey Bergfalk.
Best,
David
(KGRC) seminar talks Tuesday, March 8 and Thursday, March 10
Kurt Godel Research Center
3/3/2022 10:34:15
The KGRC welcomes as guests:
Jonathan Cancino (host: Vera Fischer) visits the KGRC from March 7 to
March 11 and give a talk (see below).
Piotr Borodulin-Nadzieja (host: Damian Sobota) visits the KGRC from March
9 to March 13.
* * *
Set Theory Research Seminar Kurt G?del Research Center Tuesday, March 8
"There may be no I-ultrafilters for any F_\sigma ideal I"
Jonathan Cancino (Czech Academy of Sciences, Czech Republic)
Given an ideal I and an ultrafilter U, both on \omega, we say that U is an
I-ultrafilter if for any f:\omega\to\omega there is A\in U such that
f[A]\in I. This notion was introduced by J. Baumgartner in 1995, and it
has proved to be very useful in the classification of combinatorial
properties of ultrafilters. In particular, the notion of Hausdorff
ultrafilter is codify as being G_fc-ultrafilter, where G_fc denotes the
ideal of finite chromatic graphs on. We will prove that consistently there
is no I-ultrafilter for any F_\sigma ideal I. Since the ideal G_fc is an
F_\sigma ideal, our result implies that consistently there is no Hausdorff
ultrafilter. This answers a question of M. Di Nasso and M. Forti, among
several other questions about the existence of I-ultrafilters.
Time and Place
Talk at 3:00pm in hybrid mode, in person as well as via Zoom.
Universit?t Wien
Institut f?r Mathematik
Kolingasse 14-16
1090 Wien
1st floor
Seminar room 10
Zoom: If you need the Zoom data and have not received the meeting link by
the day before the talk, please contact richard.springer@univie.ac.at!
(Please direct any other requests pertaining to the Set Theory Seminar and
its Zoom meeting to vera.fischer@univie.ac.at.)
Students at Uni Wien are strongly encouraged to attend the seminar in person.
* * *
Logic Colloquium
Kurt G?del Research Center
Thursday, March 10
"The Interplay of Determinacy, Large Cardinals, and Inner Models"
Sandra M?ller (TU Wien)
The standard axioms of set theory, Zermelo-Fraenkel set theory with Choice
(ZFC), do not suffice to answer all questions in mathematics. While this
follows abstractly from Kurt G?del's famous incompleteness theorems, we
nowadays know numerous concrete examples for such questions. In addition
to a large number of problems in set theory, even many problems outside of
set theory have been showed to be unsolvable, meaning neither their truth
nor their failure can be proven from ZFC. A major part of set theory is
devoted to attacking this problem by studying various extensions of ZFC
and their properties with the overall goal to identify the "right" axioms
for mathematics that settle these problems.
Determinacy assumptions are canonical extensions of ZFC that postulate the
existence of winning strategies in natural infinite two-player games. Such
assumptions are known to enhance sets of real numbers with a great deal of
canonical structure. Other natural and well-studied extensions of ZFC are
given by the hierarchy of large cardinal axioms. Inner model theory
provides canonical models for many large cardinal axioms. Determinacy
assumptions, large cardinal axioms, and their consequences are widely used
and have many fruitful implications in set theory and even in other areas
of mathematics. Many applications, in particular, proofs of consistency
strength lower bounds, exploit the interplay of determinacy axioms, large
cardinals, and inner models. In this talk I will survey recent
developments as well as my contribution to this flourishing area.
Time and Place
Talk at 3:00pm
Universit?t Wien
Institut f?r Mathematik
Lecture Hall HS 13
2nd floor
Oskar-Morgenstern-Platz 1
1090 Wien
Cross-Alps Logic Seminar (speaker: Michal Skrzypczak)
Cross-Alps Logic Seminar
3/1/2022 1:33:55
Dear all,
On Friday 04.03.2022 at 16:00
Michal Skrzypczak (University of Warsaw)
will give a talk on
The infinite tree - from Kolmogorov, Rabin, and Shelah to
modern Theoretical Computer Science
Please refer to the usual webpage of our
LogicGroup
for more details and the abstract of the talk.
The seminar will be held remotely through Webex. Here are the
information to access the meeting:
ACCESS TO WEBEX MEETING
Link
Meeting
Number Meeting: 2733 686 2768
Password: ErDGYCdk795
The Cross-Alps Logic Seminar is co-organized by the logic groups of
Genoa, Lausanne, Turin and Udine as part of our collaboration in the
project PRIN 2017 'Mathematical logic: models, sets, computability'.
All the best,
Luca
--
We sent you this email because you are in the mailing list of
Cross-Alps Logic Seminar.
If you do not want to receive our seminar announcements anymore,
please write to
luca.mottoros@unito.it.
This Week in Logic at CUNY
This Week in Logic at CUNY
2/27/2022 22:31:00
This Week in Logic at CUNY:
- - - - Monday, Feb 28, 2022 - - - -
Logic and Metaphysics WorkshopDate: Monday, February 28, 4.15-6.15 (NY time), GC 5382For meeting information (including zoom link for those wishing to attend remotely), please sign up for our mailing list at https://logic.commons.gc.cuny.edu/about/Michael Burton (Yale).
Title: Paraconsistency with some detachment
Abstract: In this talk, a proof-of-concept logic is presented that is like first-order LP (the “logic of paradox”) except things behave classically within the scope of universal quantifiers. This logic’s material conditional does not, in general, detach, but much can be deduced with it. Structures for this logic are classical first-order structures equipped with a congruence relation, giving this logic a connection to Priest’s collapsing lemma for LP. Some possible improvements to this logic are then discussed. One of these involves separating classicality from universal quantification, having classicality be mediated instead by operators that interact with variable assignments. Finally, the relevance of logics of this kind to various logical paradoxes is discussed.
- - - - Tuesday, Mar 1, 2022 - - - -
- - - - Wednesday, Mar 2, 2022 - - - -
- - - - Thursday, Mar 3, 2022 - - - -
- - - - Friday, Mar 4, 2022 - - - -
Set Theory Seminar
CUNY Graduate Center, Friday, March 4, 12:30pm
The seminar will take place virtually at 12:30pm US Eastern Standard Time. Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
Tom Benhamou, Tel Aviv University
Subforcings of the Tree-Prikry Forcing
We investigate which forcing notions can be embedded into a Tree-Prikry forcing. It turns out that the answer changes drastically under different large cardinal assumptions. We will focus on the class of κ-strategically closed forcings of cardinality κ, <κ-strategically closed forcings of cardinality κ and the κ-distributive forcing notions of cardinality κ. Then we will examine distributive subforcings of the Prikry forcing of cardinality larger than κ. This is a joint work with Moti Gitik and Yair Hayut.
Next Week in Logic at CUNY:
- - - - Monday, Mar 7, 2022 - - - -
Logic and Metaphysics Workshop
Date: Monday, March 7, 4.15-6.15 (NY time), GC 5382
For meeting information (including zoom link for those wishing to attend remotely), please sign up for our mailing list at
https://logic.commons.gc.cuny.edu/about/David Papineau (King’s).
Title: Understanding Causal Inference
Abstract: The current pandemic has focused attention on the techniques used by epidemiologists and other non-experimental scientists to infer causal hypotheses from correlational data. These techniques, which hinge on assumptions about the way causal connections manifest themselves in conditional and unconditional correlations, pose an obvious philosophical challenge. What is it about causation that allows them to work? None of the mainstream accounts of causation—counterfactual, process, dispositional, regularity—casts any light on this question. Probabilistic and interventionist theories of causation do offer a direct response to the challenge, by positing a constitutive connection between causes and correlations, but I shall argue that these theories do not dig deep enough. Instead I shall develop an older idea—which goes back to H.A. Simon in the 1950s—that relates causal relationships to systems of structural equations with probabilistically independent exogenous variables. The attraction of this structural equations approach is that it allows us to view the correlational patterns as fallible evidence for causal relationships, rather than constitutive of them. I shall consider whether this approach can lead to a full reduction of causation and how it might accommodate quantum mechanical unpredictability.
- - - - Tuesday, Mar 8, 2022 - - - -
- - - - Wednesday, Mar 9, 2022 - - - -
The New York City Category Theory Seminar
Department of Computer Science
Department of Mathematics
The Graduate Center of The City University of New York
New URL:
http://www.sci.brooklyn.cuny.edu/~noson/Seminar/index.htmlContact N Yanofsky for zoom info (
noson@sci.brooklyn.cuny.edu)
Speaker: Jin-Cheng Guu, Stony Brook University.
Date and Time: Wednesday March 9, 2022, 7:00 - 8:30 PM., on Zoom.
Title: Topological Quantum Field Theories from Monoidal Categories.
Abstract: We will introduce the notion of a topological quantum field theory (tqft) and a monoidal category. We will then construct a few (extended) tqfts from monoidal categories, and show how quantum invariants of knots and 3-manifolds were obtained. If time permits, I will discuss (higher) values in (higher) codimensions based on my recent work on categorical center of higher genera (joint with A. Kirillov and Y. H. Tham).
- - - - Thursday, Mar 10, 2022 - - - -
- - - - Friday, Mar 11, 2022 - - - -
Set Theory Seminar
CUNY Graduate Center, Friday, March 11, 12:30pm
The seminar will take place virtually at 12:30pm US Eastern Standard Time. Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
William Chan, Carnegie Mellon University
Logic Workshop
CUNY Graduate Center, Friday, March 11, 2pm
The seminar will take place at the CUNY Graduate Center at 2pm in Room TBA.
Joel David Hamkins, Notre Dame University
Infinite wordle and the mastermind numbers
I shall introduce and consider the natural infinitary variations of Wordle, Absurdle, and Mastermind. Infinite Wordle extends the familiar finite game to infinite words and transfinite play—the code-breaker aims to discover a hidden codeword selected from a dictionary Δ⊆Σω of infinite words over a countable alphabet Σ by making a sequence of successive guesswords, receiving feedback after each guess concerning its accuracy. For any dictionary using the usual 26-letter alphabet, for example, the code-breaker can win in at most 26 guesses, and more generally in n guesses for alphabets of finite size n. Meanwhile, for some dictionaries on an infinite alphabet, infinite play is required, but the code-breaker can always win by stage ω on a countable alphabet, for any fixed dictionary. Infinite Mastermind, in contrast, is a subtler game than Wordle because only the number and not the position of correct bits is given. When duplication of colors is allowed, nevertheless, then the code-breaker can still always win by stage ω, but in the no-duplication variation, no countable number of guesses (even transfinite) is sufficient for the code-breaker to win. I therefore introduce the mastermind number, denoted mm, to be the size of the smallest winning no-duplication Mastermind guessing set, a new cardinal characteristic of the continuum, which I prove is bounded below by the additivity number add(M) of the meager ideal and bounded above by the covering number cov(M). In particular, the precise value of the mastermind number is independent of ZFC and can consistently be strictly between ℵ1 and the continuum 2ℵ0. In simplified Mastermind, where the feedback given at each stage includes only the numbers of correct and incorrect bits (omitting information about rearrangements), then the corresponding simplified mastermind number is exactly the eventually different number d(≠∗). http://jdh.hamkins.org/infinite-wordle-and-the-mastermind-numbers-cuny-logic-workshop-march-2022/
- - - - Other Logic News - - - -
- - - - Web Site - - - -
"Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)"
-------- ADMINISTRIVIA --------
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Wednesday seminar
Prague Set Theory Seminar
2/27/2022 14:13:12
Dear all,
The seminar meets on Wednesday February 2nd at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program:
Noé de Rancourt -- On countable unions of Borel equivalence relations
I'll talk about dichotomies of Borel equivalence relations obtained with
Benjamin Miller which characterize the obstructions for an equivalence
relation to be in a given complexity class F assuming we know it is a
countable union of relations from F. Our simplest result is in some
sense an extension of Kechris-Louveau's E_1-dichotomy. There will be no
proofs, because those are way too long.
Best,
David
European Set Theory Conference: 29 August - 2 September 2022
Conference
2/25/2022
EUROPEAN SET THEORY CONFERENCE 2022
August 29th-September 2nd, 2022
Turin, Italy
We are pleased to announce that the registration for the ESTC2022 is now open! (See below for the relevant deadlines.) Various forms of financial support for young researchers are available. It is also possible to submit a title and abstract for a contributed talk; submissions will be evaluated by the Scientific Committee, and a decision will be communicated 2-3 months before the conference. Please visit our website or contact us through this form for more information.
The conference will be held in person, we are confident that at the end of the summer the pandemic situation will be under control. It will be nice to meet in person again, after these challenging years. Also, it is a very good season to visit Turin, a beautiful city in northern Italy, while attending one of the most exciting conferences in set theory!
If you are interested, please register as soon as possible, and do not forget to submit your title and abstract if you want to contribute with a short talk. We also kindly ask you to share this announcement with all people who might be interested in the event.
IMPORTANT DEADLINES:
30/04/2022: Abstract submission for contributed talks
30/06/2022: Early registration with reduced fee
22/08/2022: Registration
MORE ON THE CONFERENCE:
The European Set Theory Conferences is a series of biannual meetings coordinated by the European Set Theory Society (ESTS). This year's edition is organized by the Department of Mathematics of the University of Turin and ESTS, in partnership with the Clay Mathematics Institute. It is the most important conference in set theory, and gathers the worldwide leaders in the field as well as many young researchers. During the event, the prestigious Hausdorff medal will be awarded for the most influential work in set theory published in the preceding five years. There will also be a special session in honor of Boban Veličković's 60th birthday.
Invited speakers
- Jeffrey Bergfalk (Vienna)
- Filippo Calderoni (Chicago)
- Natasha Dobrinen (Denver)
- Osvaldo Guzmán (Mexico)
- Joel Hamkins (Notre Dame)
- Chris Lambie-Hanson (Prague)
- Martino Lupini (New Zealand)
- Julien Melleray (Lyon)
- Andrew Marks (UCLA)
- Sandra Müller (Vienna)
- Saharon Shelah (Jerusalem)
- Stevo Todorčević (Toronto and Paris)
- Jouko Väänänen (Helsinki)
- Zoltán Vidnyánsky (Caltech)
- Trevor Wilson (Miami)
Tutorials
- Yair Hayut (Jerusalem)
- Grigor Sargsyan (Poland)
Boban Veličković's 60th Birthday Celebration
- Laura Fontanella (Paris)
- Rahman Mohammadpour (Vienna)
- Giorgio Venturi (Brasil)
- Matteo Viale (Turin)
Scientific committee
Joan Bagaria (chair), Matthew Foreman, Moti Gitik, Péter Komjáth, Piotr Koszmider, Heike Mildenberger, Luca Motto Ros, John Steel
Local organizing committee
Alessandro Andretta, Raphaël Carroy, Luca Motto Ros, Gianluca Paolini, Francesco Parente, Salvatore Scamperti, Matteo Viale
Tagged: Jeffrey Bergfalk, Filippo Calderoni, Natasha Dobrinen, Osvaldo Guzmán, Joel Hamkins, Chris Lambie-Hanson, Martino Lupini, Julien Melleray, Andrew Marks, Sandra Müller, Saharon Shelah, Stevo Todorčević, Jouko Väänänen, Zoltán Vidnyánsky, Trevor Wilson, Yair Hayut, Grigor Sargsyan, Laura Fontanella, Rahman Mohammadpour, Giorgio Venturi, Matteo Viale,
Logic Seminar Wed 2 March 2022 16:00 hrs at NUS by Lavinia Picollo
NUS Logic Seminar
2/25/2022 4:11:42
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 2 March 2022, 16:00 hrs
Talk via Zoom:
https://nus-sg.zoom.us/j/83049258042?pwd=UWViaWNvTFUrdFdhOHJCdEVydnVkdz09
Meeting ID: 830 4925 8042
Passcode: 1729=x3+y3
Speaker: Lavinia Picollo, NUS
Title: High-order logic and disquotational truth
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract:
Truth predicates are widely believed to be capable of serving
a certain logical or quasi-logical function. There is little consensus,
however, on the exact nature of this function. We offer a series of
formal results in support of the thesis that disquotational truth is
a device to simulate higher-order resources in a first-order setting.
More specifically, we show that any theory formulated in a higher-order
language can be naturally and conservatively interpreted in a
first-order theory with a disquotational truth or truth-of predicate.
In the first part of the talk we focus on the relation between truth
and full impredicative sentential quantification. The second part
is devoted to the relation between truth-of and full impredicative
predicate quantification.
This is joint work with Thomas Schindler
(KGRC) Set Theory Seminar talk on Tuesday, March 1
Kurt Godel Research Center
2/24/2022 4:42:57
The KGRC welcomes as guests:
Sarka Stejskalova and Radek Honzik (host: Sy-David Friedman) visit the KGRC
until February 28.
* * *
Set Theory Research Seminar
Kurt G?del Research Center
Tuesday, March 1
"Ramsey Theory of Ordinals and Finite Combinatorics"
Thilo Weinert (KGRC)
The Ramsey Theory of Ordinals has been investigated over the last decades and a
large variety of results have been attained. The talk is going to focus on the
Ramsey Theory of finite multiples both of infinite cardinals and, in some cases
products of two infinite cardinals. This leads to problems in finite
combinatorics similar to the calculation of finite Ramsey numbers. On the one
hand, exact results are usually only obtainable if the natural numbers involved
remain somewhat small. On the other hand, sometimes asymptotic results can be
attained.
More concretely, for any ordinal $\alpha$ and $\beta$, let $r(\alpha, \beta)$
denote the least ordinal $\gamma$ such that any colouring of the pairs in
$\gamma$ in black and white either allows for a homogeneously white subset of
order-type $\alpha$ or a homogeneously black subset of order-type $\beta$.
Since the nineties it is known that the growth of $r(n, 3)$ is of order
$n^2/log(n)$. It turns out that for any infinite cardinal $\lambda$, we have
$r(\lambda * n, 3) = \lambda * r(I_n, L_3)$ where the growth of $r(I_n, L_3)$
is of order $n^2/log(n)$ as well. Similarly, if $\kappa > \lambda$ is weakly
compact, we have $r(\kappa * \lambda * n, 3) = \kappa * \lambda * r(I_n, S_3)
where, again, the growth of $r(I_n, L_3)$ is of order $n^2/log(n)$. Finally
there is a finitary characterisation of the Ramsey numbers $r(\omega^2 *n, k)$
for natural numbers $n$ and $k$. However the growth behaviour of $r(\omega^2 *
n, 3)$ is still unknown.
This is partly joint work with Ferdinand Ihringer and Deepak Rajendraprasad.
Time and Place
Talk at 3:00pm in hybrid mode, in person as well as via Zoom.
Universitt Wien
Institut f?r Mathematik
Kolingasse 14-16
1090 Wien
2nd floor
Seminar room 10
Talk at 3:00pm -- if you need the Zoom data and have not received the
meeting link by the day before the talk, please contact
richard.springer@univie.ac.at! (Please direct any other requests
pertaining to the Set Theory Seminar and its Zoom meeting to
vera.fischer@univie.ac.at.)
Students at Uni Wien are strongly encouraged to attend the seminar in person.
* * *
Logic Colloquium
Kurt G?del Research Center
Please note that Sandra M?llers talk had to be rescheduled to March 10.
Two CMU seminars next Tuesday
Carnegie Mellon Logic Seminar
2/22/2022 21:06:53
TUESDAY, March 1, 2022
Mathematical logic seminar: 3:30 P.M., Online, Aristotelis
Panagiotopoulos, Carnegie Mellon University
Join Zoom Meeting:
https://cmu.zoom.us/j/92655324096?pwd=VUhSSlkrdHMxbTlSYUMxYzFXM01kdz09
Meeting ID: 926 5532 4096
Passcode: 555455
TITLE: Every CBER is smooth below a Milliken-generic strong subtree (Part
I)
ABSTRACT: The theory of Borel reductions becomes a very delicate subject
of study when one restricts attention to the class of Countable Borel
Equivalence Relations (CBERs). Indeed, no matter how complex a CBER is,
its complexity tends to reside on a "small" piece of its domain. For
example a result of Hjorth and Kechris states that every CBER on a Polish
space is hyperfinite when restricted to some comeager set. Similarly,
classical results of Mathias about forcing extensions by Mathias reals
imply that every CBER on the Ellentuck Ramsey space is hyperfinite when
restricted to some pure Ellentuck cube. In this talk we show that the
Milliken space M of strong trees satisfies a much stronger canonization
property: if E is CBER on M then for the Milliken-generic T in M we have
that E and = agree on the pure Milliken cube [T].
This is joint work with Allison Wang.
TUESDAY, March 1, 2022
Set theory reading group: 4:30 P.M., Online, Allison Wang, Carnegie
Mellon University
Join Zoom Meeting:
https://cmu.zoom.us/j/92655324096?pwd=VUhSSlkrdHMxbTlSYUMxYzFXM01kdz09
Meeting ID: 926 5532 4096
Passcode: 555455
TITLE: Every CBER is smooth below a Milliken-generic strong subtree (Part
II)
ABSTRACT: The theory of Borel reductions becomes a very delicate subject
of study when one restricts attention to the class of Countable Borel
Equivalence Relations (CBERs). Indeed, no matter how complex a CBER is,
its complexity tends to reside on a "small" piece of its domain. For
example a result of Hjorth and Kechris states that every CBER on a Polish
space is hyperfinite when restricted to some comeager set. Similarly,
classical results of Mathias about forcing extensions by Mathias reals
imply that every CBER on the Ellentuck Ramsey space is hyperfinite when
restricted to some pure Ellentuck cube. In this talk we show that the
Milliken space M of strong trees satisfies a much stronger canonization
property: if E is CBER on M then for the Milliken-generic T in M we have
that E and = agree on the pure Milliken cube [T].
This is joint work with Aristotelis Panagiotopoulos.
This Week in Logic at CUNY
This Week in Logic at CUNY
2/20/2022 22:30:00
This Week in Logic at CUNY:
- - - - Monday, Feb 21, 2022 - - - -
- - - - Tuesday, Feb 22, 2022 - - - -
- - - - Wednesday, Feb 23, 2022 - - - -
Speaker: David Roberts.
Date and Time: Wednesday February 23, 2022, 7:00 - 8:30 PM., on Zoom.
Title: Do you have what it takes to use the diagonal argument?
Abstract: Lawvere's reformulation of the diagonal argument captured many instances from the literature in an elegant and abstract category-theoretic treatment. The original version used cartesian closed categories, but gave a nod to how the statement of the argument could be adjusted so as to make fewer demands on the category. In fact the argument, and the fixed-point theorem that Lawvere provided as the positive version of the argument, both require much less than Lawvere stated. This talk will give an outline of Lawvere's version of the diagonal argument, his corresponding fixed-point theorem, and then cover a few versions obtained recently that drop assumptions on the properties/structure of the category at hand.
- - - - Thursday, Feb 24, 2022 - - - -
- - - - Friday, Feb 25, 2022 - - - -
Set Theory Seminar
CUNY Graduate Center, Friday, February 25, 12:30pm
The seminar will take place virtually at 12:30pm US Eastern Standard Time. Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
Richard Matthews, University of Leeds
Big classes and the respected model
In standard (ZFC) set theory, proper classes are not sets because they are too 'big' or, to put it in a formal way, because they surject onto any non-zero ordinal. We shall study this notion of 'bigness' in weaker systems of set theory, in particular those in which the Power Set Axiom fails. We will observe that in many such theories it is possible to have proper classes which are not big.
As part of this, we shall see a failed attempt to find a proper class which is not big in the theory ZF without Power Set but with Collection - which is by taking a certain symmetric submodel of a class forcing. It will turn out that this approach fails because, unlike in the set forcing case, the symmetric submodel of a class forcing need not exhibit many of the nice properties that we would expect. Notably, Collection may fail and, in fact, it is unclear which axioms need necessarily hold.
This will lead to the definition of the 'Respected Model', an alternative approach to defining a submodel of a class forcing in which Choice fails. We will investigate the properties of this new model and compare it to the symmetric version.
- - - - Monday, Feb 28, 2022 - - - -
Logic and Metaphysics WorkshopDate: Monday, February 28, 4.15-6.15 (NY time), GC 5382For meeting information, please sign up for our mailing list at https://logic.commons.gc.cuny.edu/about/Michael Burton (Yale).
Title: Paraconsistency with some detachment
Abstract: In this talk, a proof-of-concept logic is presented that is like first-order LP (the “logic of paradox”) except things behave classically within the scope of universal quantifiers. This logic’s material conditional does not, in general, detach, but much can be deduced with it. Structures for this logic are classical first-order structures equipped with a congruence relation, giving this logic a connection to Priest’s collapsing lemma for LP. Some possible improvements to this logic are then discussed. One of these involves separating classicality from universal quantification, having classicality be mediated instead by operators that interact with variable assignments. Finally, the relevance of logics of this kind to various logical paradoxes is discussed.
- - - - Tuesday, Mar 1, 2022 - - - -
- - - - Wednesday, Mar 2, 2022 - - - -
- - - - Thursday, Mar 3, 2022 - - - -
- - - - Friday, Mar 4, 2022 - - - -
Set Theory Seminar
CUNY Graduate Center, Friday, March 4, 12:30pm
The seminar will take place virtually at 12:30pm US Eastern Standard Time. Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
Tom Benhamou, Tel Aviv University
- - - - Other Logic News - - - -
- - - - Web Site - - - -
"Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)"
-------- ADMINISTRIVIA --------
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jreitz@nylogic.org.
Next CMU math logic seminar
Carnegie Mellon Logic Seminar
2/18/2022 11:58:13
TUESDAY, February 22, 2022
Mathematical logic seminar: 3:30 P.M., Online, Sam Sanders,
Ruhr-Universitaet Bochum
Join Zoom Meeting:
https://cmu.zoom.us/j/92655324096?pwd=VUhSSlkrdHMxbTlSYUMxYzFXM01kdz09
Meeting ID: 926 5532 4096
Passcode: 555455
TITLE: The two-dimensional nature of ordinary mathematics
ABSTRACT: The usual foundations of mathematics (ZFC set theory) are
'two-dimensional' in nature in that given a theorem T provable in ZFC, the
following two questions are unavoidable:
a) is T provable in ZF alone?
b) If not, which fragment of the Axiom of Choice (AC) does T imply?
One reason to make this distinction is that the choice functions from AC
are fundamentally non-constructive in nature (even relative to ZF).
We show that ordinary mathematics, when formulated in the language of
third-order arithmetic, is similarly two-dimensional in nature in that the
following questions are fundamental for a theorem S:
c) Is S provable from (conventional) comprehension alone?
d) If not, which fragment of the neighborhood function principle (NFP)
does S imply?
Intellectually pleasing, NFP is a fragment of AC with continuous choice
functions, i.e. provable in ZF (and much weaker systems). We discuss the
weakest principle falling under d), namely the uncountability of R, and
how NFP gives rise to a new computational model for comparing theorems of
ordinary mathematics. This is joint work with Dag Normann.
Wednesday seminar
Prague Set Theory Seminar
2/18/2022 11:43:49
Dear all,
The seminar meets on Wednesday February 23rd at 11:00 in the Institute
of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: Jindrich Zapletal -- Geometric set theory II
This is a continuation from the previous week. I will prove a couple of
basic feature of balanced extensions of the Solovay model: they add no
new sets of ordinals and contain no MAD families in particular. I will
also produce the first example of a consistency result: it is consistent
with ZF+DC to have a Hamel basis for R over Q, but no nonprincipal
ultrafilter on natural numbers.
Best,
David
Logic Seminar today at 16:30 hrs
NUS Logic Seminar
2/16/2022 2:52:47
Hello, a short reminder that the logic seminar today starts at
16:30 hrs Singapore time, not at the full hour as usual.
Regards, Frank
Wednesday seminar
Prague Set Theory Seminar
2/14/2022 3:51:55
Dear all,
The seminar meets on Wednesday February 16th at 11:00 in the Institute
of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: Jindřich Zapletal -- Geometric Set Theory
I will explain basics of the method developed with Paul Larson which
obtains consistency results in choiceless set theory ZF+DC using
definable forcing extensions of the Solovay model. Among recent
applications, if n>0 is a natural number and Gn is the graph on
n-dimensional Euclidean space connecting points of rational distance, it
is consistent with ZF+DC that Gn has countable chromatic number while
Gn+1 does not.
Best,
David
Logic Seminar Wed 16 February 2022 16:30 hrs by Rupert Hoelzl
NUS Logic Seminar
2/14/2022 0:48:34
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 16 February 2022, 16:30 hrs
Talk via Zoom:
https://nus-sg.zoom.us/j/83049258042?pwd=UWViaWNvTFUrdFdhOHJCdEVydnVkdz09
Meeting ID: 830 4925 8042
Passcode: 1729=x3+y3
Speaker: Rupert Hoelzl, Universitaet der Bundeswehr, Muenchen
Title: Universality, optimality and randomness deficiency
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract: A Martin-Loef test U is universal if it captures all
sequences which are not Martin-Loef random. It is optimal if
for every Martin-Loef test V there is a constant c
such that, for all n, V_{n+c} subseteq U_n. We study the
computational differences between universal and optimal
Martin-Loef tests as well as the effects of these differences
on both the notions of layerwise computability and the Weihrauch degree
of LAY, the function that produces a bound on the randomness
deficiency of a given Martin-Loef random sequence. We prove several
robustness and idempotence results concerning the Weihrauch degree of
LAY and we show that layerwise computability is
more restrictive than Weihrauch reducibility to LAY. Along similar
lines, we also study the principle RD, a variant of LAY
outputting the precise randomness deficiency of sequences instead of
only an upper bound as LAY.
This is joint work with Paul Shafer.
The paper is available as in the Annals of Pure and Applied Logic,
https://doi.org/10.1016/j.apal.2015.05.006
Logic Seminar Wed 16 February 2022 16:30 hrs by Rupert Hoelzl
NUS Logic Seminar
2/14/2022 0:49:39
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 16 February 2022, 16:30 hrs
Talk via Zoom:
https://nus-sg.zoom.us/j/83049258042?pwd=UWViaWNvTFUrdFdhOHJCdEVydnVkdz09
Meeting ID: 830 4925 8042
Passcode: 1729=x3+y3
Speaker: Rupert Hoelzl, Universitaet der Bundeswehr, Muenchen
Title: Universality, optimality and randomness deficiency
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract: A Martin-Loef test U is universal if it captures all
sequences which are not Martin-Loef random. It is optimal if
for every Martin-Loef test V there is a constant c
such that, for all n, V_{n+c} subseteq U_n. We study the
computational differences between universal and optimal
Martin-Loef tests as well as the effects of these differences
on both the notions of layerwise computability and the Weihrauch degree
of LAY, the function that produces a bound on the randomness
deficiency of a given Martin-Loef random sequence. We prove several
robustness and idempotence results concerning the Weihrauch degree of
LAY and we show that layerwise computability is
more restrictive than Weihrauch reducibility to LAY. Along similar
lines, we also study the principle RD, a variant of LAY
outputting the precise randomness deficiency of sequences instead of
only an upper bound as LAY.
This is joint work with Paul Shafer.
The paper is available as in the Annals of Pure and Applied Logic,
https://doi.org/10.1016/j.apal.2015.05.006
This Week in Logic at CUNY
This Week in Logic at CUNY
2/13/2022 22:38:00
This Week in Logic at CUNY:
- - - - Monday, Feb 14, 2022 - - - -
Logic and Metaphysics WorkshopDate: Monday, February 14, 4.15-6.15 (NY time), GC 5382For meeting information, please sign up for our mailing list at https://logic.commons.gc.cuny.edu/about/Ekaterina Kubyshkina (Campinas)
Title: Ignorance as an excuse, formally
Abstract: In the current literature on epistemology there is a lively debate on which type of ignorance may provide a moral excuse. A good candidate is the one in which an agent has never considered or thought about a true proposition p. From a logical perspective, it is usual to model situations involving ignorance by means of epistemic logic. However, no formal analysis was provided for ignorance as an excuse. First, we will argue that if ignorance is expressed via standard modalities of knowledge and belief, one is unable to represent ignorance as an excuse. Secondly, we fill this gap by providing an original logical setting for modelling this type of ignorance. In particular, we introduce a complete and sound logic in which ignorance is expressed as a primitive modality. Semantically, the logic is characterized by Kripke semantics with possibly incomplete worlds. Moreover, in order to consider the conditions of a possible change of an agent’s ignorance, we will extend the setting by considering public announcements.
- - - - Tuesday, Feb 15, 2022 - - - -
- - - - Wednesday, Feb 16, 2022 - - - -
Date and Time: Wednesday February 16, 2022, 7:00 - 8:30 PM., IN PERSON MEETING, GC Room 6417.
Speaker: Emilio Minichiello, CUNY Graduate Center.
Title: Category Theory ∩ Differential Geometry.
· Abstract: In this talk we will take a tour through some areas of math at the intersection of category theory and differential geometry. We will talk about how the use of category theory works towards solving 2 problems: 1) to give rigorous definitions and techniques to study increasingly complicated objects in differential geometry that are coming from physics, like orbifolds and bundle gerbes, and 2) to find good categories in which to embed the category of finite dimensional smooth manifolds, without losing too much geometric intuition. This involves the study of Lie groupoids, sheaves, diffeological spaces, stacks, and infinity stacks. I will try to motivate the use of these mathematical objects and how they help mathematicians understand differential geometry and expand its scope.
- - - - Thursday, Feb 17, 2022 - - - -
- - - - Friday, Feb 18, 2022 - - - -
Set Theory Seminar
CUNY Graduate Center, Friday, February 18, 12:30pm
The seminar will take place virtually at 12:30pm US Eastern Standard Time. Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
Sittinon Jirattikansakul, Tel Aviv University
Forcing with overlapping supercompact extenders: Part II
In the paper 'Blowing up the power of a singular cardinal of uncountable cofinality', Gitik introduced the forcing which can violate the SCH at singular cardinals of any cofinalities, assuming that the singular cardinals are also singular in the ground model. The forcing is built up from a Mitchell increasing sequence of strong extenders, and it preserves all cardinals and cofinalities in the generic extension. In this talk, we will discuss a forcing which is built from a Mitchell increasing sequence of supercompact extenders. The forcing also violates the SCH at singular cardinals of any cofinalities which are singular in the ground model. An important feature of this forcing is that it is possible to collapse the successor of a singular cardinal, while preserving cardinals above it.
Next Week in Logic at CUNY:
- - - - Monday, Feb 21, 2022 - - - -
- - - - Tuesday, Feb 22, 2022 - - - -
- - - - Wednesday, Feb 23, 2022 - - - -
Speaker: David Roberts.
Date and Time: Wednesday February 23, 2022, 7:00 - 8:30 PM., on Zoom.
Title: Do you have what it takes to use the diagonal argument?
Abstract: Lawvere's reformulation of the diagonal argument captured many instances from the literature in an elegant and abstract category-theoretic treatment. The original version used cartesian closed categories, but gave a nod to how the statement of the argument could be adjusted so as to make fewer demands on the category. In fact the argument, and the fixed-point theorem that Lawvere provided as the positive version of the argument, both require much less than Lawvere stated. This talk will give an outline of Lawvere's version of the diagonal argument, his corresponding fixed-point theorem, and then cover a few versions obtained recently that drop assumptions on the properties/structure of the category at hand.
- - - - Thursday, Feb 24, 2022 - - - -
- - - - Friday, Feb 25, 2022 - - - -
Set Theory Seminar
CUNY Graduate Center, Friday, February 25, 12:30pm
The seminar will take place virtually at 12:30pm US Eastern Standard Time. Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
Richard Matthews, University of Leeds
- - - - Other Logic News - - - -
- - - - Web Site - - - -
"Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)"
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to
jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email
jreitz@nylogic.org.
Next two CMU math logic seminars
Carnegie Mellon Logic Seminar
2/11/2022 19:01:40
TUESDAY, February 15, 2022
Mathematical logic seminar: 3:30 P.M., Online, Dag Normann, University of
Oslo
Join Zoom Meeting:
https://cmu.zoom.us/j/92655324096?pwd=VUhSSlkrdHMxbTlSYUMxYzFXM01kdz09
Meeting ID: 926 5532 4096
Passcode: 555455
TITLE: The complexity of operators constructed in mainstream mathematics
ABSTRACT: In an ongoing project with Sam Sanders, we have analysed third
order theorems in mainstream mathematics both from the viewpoints of
Kohlenbach's higher order reverse mathematics and Kleene's higher order
computability theory.
Based on case studies involving theorems like the Heine-Borel theorem,
Lindelöf's lemma and the Jordan decomposition theorem we observe that
constructions in mainstream mathematics give rise to natural functionals
of type three of a kind that hitherto has remained unobserved in higher
order computability theory.
In this talk we will discuss both such case studies and a possible
complexity/computability model useful for discussing the nature of such
operators.
TUESDAY, February 22, 2022
Mathematical logic seminar: 3:30 P.M., Online, Sam Sanders,
Ruhr-Universitaet Bochum
Join Zoom Meeting:
https://cmu.zoom.us/j/92655324096?pwd=VUhSSlkrdHMxbTlSYUMxYzFXM01kdz09
Meeting ID: 926 5532 4096
Passcode: 555455
TITLE: The two-dimensional nature of ordinary mathematics
ABSTRACT: The usual foundations of mathematics (ZFC set theory) are
'two-dimensional' in nature in that given a theorem T provable in ZFC, the
following two questions are unavoidable:
a) is T provable in ZF alone?
b) If not, which fragment of the Axiom of Choice (AC) does T imply?
One reason to make this distinction is that the choice functions from AC
are fundamentally non-constructive in nature (even relative to ZF).
We show that ordinary mathematics, when formulated in the language of
third-order arithmetic, is similarly two-dimensional in nature in that the
following questions are fundamental for a theorem S:
c) Is S provable from (conventional) comprehension alone?
d) If not, which fragment of the neighborhood function principle (NFP)
does S imply?
Intellectually pleasing, NFP is a fragment of AC with continuous choice
functions, i.e. provable in ZF (and much weaker systems). We discuss the
weakest principle falling under d), namely the uncountability of R, and
how NFP gives rise to a new computational model for comparing theorems of
ordinary mathematics. This is joint work with Dag Normann.
This Week in Logic at CUNY
This Week in Logic at CUNY
2/6/2022 22:30:00
This Week in Logic at CUNY:
- - - - Monday, Feb 7, 2022 - - - -
Logic and Metaphysics WorkshopDate: Monday, February 7, 4.15-6.15 (NY time), GC 5382For meeting information, please sign up for our mailing list at https://logic.commons.gc.cuny.edu/about/Guillermo Badia (Queensland)
Title: Frame Definability in Finitely-Valued Modal Logics
Abstract: In this paper we study frame definability in finitely-valued modal logics and establish two main results via suitable translations: (1) in finitely-valued modal logics one cannot define more classes of frames than are already definable in classical modal logic, and (2) a large family of finitely-valued modal logics define exactly the same classes of frames as classical modal logic (including modal logics based on finite Heyting and MV-algebras). In this way one may observe, for example, that the celebrated Goldblatt–Thomason theorem applies immediately to these logics. In particular, we obtain the central result from [B. Teheux. Modal definability for Łukasiewicz validity relations. Studia Logica 104 (2): 343–363 (2016)] with a much simpler proof and answer one of the open questions left in that paper. Moreover, the proposed translations allow us to determine the computational complexity of a big class of finitely-valued modal logics.
Note: This is joint work with Carles Noguera and Xavier Caicedo.
- - - - Tuesday, Feb 8, 2022 - - - -
- - - - Wednesday, Feb 9, 2022 - - - -
- - - - Thursday, Feb 10, 2022 - - - -
- - - - Friday, Feb 11, 2022 - - - -
Set Theory Seminar
CUNY Graduate Center, Friday, February 11, 12:30pm
The seminar will take place virtually at 12:30pm US Eastern Standard Time. Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
Sittinon Jirattikansakul, Tel Aviv University
Forcing with overlapping supercompact extenders
In the paper 'Blowing up the power of a singular cardinal of uncountable cofinality', Gitik introduced the forcing which can violate the SCH at singular cardinals of any cofinalities, assuming that the singular cardinals are also singular in the ground model. The forcing is built up from a Mitchell increasing sequence of strong extenders, and it preserves all cardinals and cofinalities in the generic extension. In this talk, we will discuss a forcing which is built from a Mitchell increasing sequence of supercompact extenders. The forcing also violates the SCH at singular cardinals of any cofinalities which are singular in the ground model. An important feature of this forcing is that it is possible to collapse the successor of a singular cardinal, while preserving cardinals above it.
Next Week in Logic at CUNY:
- - - - Monday, Feb 14, 2022 - - - -
Logic and Metaphysics WorkshopDate: Monday, February 14, 4.15-6.15 (NY time), GC 5382For meeting information, please sign up for our mailing list at https://logic.commons.gc.cuny.edu/about/Ekaterina Kubyshkina (Campinas)
Title: Ignorance as an excuse, formally
Abstract: In the current literature on epistemology there is a lively debate on which type of ignorance may provide a moral excuse. A good candidate is the one in which an agent has never considered or thought about a true proposition p. From a logical perspective, it is usual to model situations involving ignorance by means of epistemic logic. However, no formal analysis was provided for ignorance as an excuse. First, we will argue that if ignorance is expressed via standard modalities of knowledge and belief, one is unable to represent ignorance as an excuse. Secondly, we fill this gap by providing an original logical setting for modelling this type of ignorance. In particular, we introduce a complete and sound logic in which ignorance is expressed as a primitive modality. Semantically, the logic is characterized by Kripke semantics with possibly incomplete worlds. Moreover, in order to consider the conditions of a possible change of an agent’s ignorance, we will extend the setting by considering public announcements.
- - - - Tuesday, Feb 15, 2022 - - - -
- - - - Wednesday, Feb 16, 2022 - - - -
Date and Time: Wednesday February 16, 2022, 7:00 - 8:30 PM., IN PERSON MEETING, GC Room 6417.
Speaker: Emilio Minichiello, CUNY Graduate Center.
Title: Category Theory ∩ Differential Geometry.
· Abstract: In this talk we will take a tour through some areas of math at the intersection of category theory and differential geometry. We will talk about how the use of category theory works towards solving 2 problems: 1) to give rigorous definitions and techniques to study increasingly complicated objects in differential geometry that are coming from physics, like orbifolds and bundle gerbes, and 2) to find good categories in which to embed the category of finite dimensional smooth manifolds, without losing too much geometric intuition. This involves the study of Lie groupoids, sheaves, diffeological spaces, stacks, and infinity stacks. I will try to motivate the use of these mathematical objects and how they help mathematicians understand differential geometry and expand its scope.
- - - - Thursday, Feb 17, 2022 - - - -
- - - - Friday, Feb 18, 2022 - - - -
Set Theory Seminar
CUNY Graduate Center, Friday, February 18, 12:30pm
The seminar will take place virtually at 12:30pm US Eastern Standard Time. Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
Sittinon Jirattikansakul, Tel Aviv University
Forcing with overlapping supercompact extenders: Part II
In the paper 'Blowing up the power of a singular cardinal of uncountable cofinality', Gitik introduced the forcing which can violate the SCH at singular cardinals of any cofinalities, assuming that the singular cardinals are also singular in the ground model. The forcing is built up from a Mitchell increasing sequence of strong extenders, and it preserves all cardinals and cofinalities in the generic extension. In this talk, we will discuss a forcing which is built from a Mitchell increasing sequence of supercompact extenders. The forcing also violates the SCH at singular cardinals of any cofinalities which are singular in the ground model. An important feature of this forcing is that it is possible to collapse the successor of a singular cardinal, while preserving cardinals above it.
- - - - Other Logic News - - - -
- - - - Web Site - - - -
"Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)"
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to
jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email
jreitz@nylogic.org.
Logic Seminar Wed 9 Feb 2022 16:00 hrs at NUS by Xie Ruofei
NUS Logic Seminar
2/6/2022 18:59:10
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 9 February 2022, 16:00 hrs
Talk via Zoom:
https://nus-sg.zoom.us/j/83049258042?pwd=UWViaWNvTFUrdFdhOHJCdEVydnVkdz09
Meeting ID: 830 4925 8042
Passcode: 1729=x3+y3
Speaker: Xie Ruofei
Title: Convergence property and randomness
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract: Consider the sum of the series (-1)^{x_n}a_n over n, where x_n
is a binary sequence and a_n is a sequence of real numbers.
We say the sequence x_n has convergence property if the sum above
converges for every computable sequence of real numbers whose sum
\sum_n a_n^2 converges computably.
Downey, Greenberg, and Tanggara showed in their unpublished paper that
every Schnorr random series x_n has convergence property.
In this talk, we will focus on convergence property and show its
similarities and differences with randomness.
This is joint work with Noam Greenberg.
Wednesday seminar
Prague Set Theory Seminar
2/4/2022 11:18:16
Dear all,
The seminar meets on Wednesday February 9th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: Jonathan Cancino -- There may be no I-ultrafilter for any
F_sigma ideal I (continued)
The notion of I-ultrafilter was introduced by Baumgartner, and it has
been useful in providing a framework for classifying many combinatorial
properties of ultrafilters. In this talk we prove, however, that the
class of F_sigma ideals may provide a vacuous classification of the
combinatorial properties of ultrafilters, that is, F_sigma ideals may be
not useful in providing combinatorial information about ultrafilters.
This in turn implies that consistently there is no Hausdorff
ultrafilter, thus answering a classical question of M. Di Nasso and M.
Forti.
Best,
David
This Week in Logic at CUNY
This Week in Logic at CUNY
1/30/2022 22:38:00
Welcome back, everyone!
- Jonas
This Week in Logic at CUNY:
- - - - Monday, Jan 31, 2022 - - - -
- - - - Tuesday, Feb 1, 2022 - - - -
- - - - Wednesday, Feb 02, 2022 - - - -
- - - - Thursday, Feb 03, 2022 - - - -
- - - - Friday, Feb 04, 2022 - - - -
Next Week in Logic at CUNY:
- - - - Monday, Feb 7, 2022 - - - -
Logic and Metaphysics WorkshopDate: Monday, February 7, 4.15-6.15 (NY time), GC 5382For meeting information, please sign up for our mailing list at https://logic.commons.gc.cuny.edu/about/Guillermo Badia (Queensland)
Title: Frame Definability in Finitely-Valued Modal Logics
Abstract: In this paper we study frame definability in finitely-valued modal logics and establish two main results via suitable translations: (1) in finitely-valued modal logics one cannot define more classes of frames than are already definable in classical modal logic, and (2) a large family of finitely-valued modal logics define exactly the same classes of frames as classical modal logic (including modal logics based on finite Heyting and MV-algebras). In this way one may observe, for example, that the celebrated Goldblatt–Thomason theorem applies immediately to these logics. In particular, we obtain the central result from [B. Teheux. Modal definability for Łukasiewicz validity relations. Studia Logica 104 (2): 343–363 (2016)] with a much simpler proof and answer one of the open questions left in that paper. Moreover, the proposed translations allow us to determine the computational complexity of a big class of finitely-valued modal logics.
Note: This is joint work with Carles Noguera and Xavier Caicedo.
- - - - Tuesday, Feb 8, 2022 - - - -
- - - - Wednesday, Feb 9, 2022 - - - -
- - - - Thursday, Feb 10, 2022 - - - -
- - - - Friday, Feb 11, 2022 - - - -
Set Theory Seminar
CUNY Graduate Center, Friday, February 11, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
Sittinon Jirattikansakul, Tel Aviv University
Forcing with overlapping supercompact extenders
In the paper 'Blowing up the power of a singular cardinal of uncountable cofinality', Gitik introduced the forcing which can violate the SCH at singular cardinals of any cofinalities, assuming that the singular cardinals are also singular in the ground model. The forcing is built up from a Mitchell increasing sequence of strong extenders, and it preserves all cardinals and cofinalities in the generic extension. In this talk, we will discuss a forcing which is built from a Mitchell increasing sequence of supercompact extenders. The forcing also violates the SCH at singular cardinals of any cofinalities which are singular in the ground model. An important feature of this forcing is that it is possible to collapse the successor of a singular cardinal, while preserving cardinals above it.
- - - - Other Logic News - - - -
- - - - Web Site - - - -
"Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)"
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jreitz@nylogic.org.
Logic Seminar 3 February 2022 16:00 hrs at NUS by Andre Nies
NUS Logic Seminar
1/27/2022 22:00:54
Invitation to the Logic Seminar at the National University of Singapore
Date: Thursday, 3 February 2022, 16:00 hrs
Talk via Zoom:
https://nus-sg.zoom.us/j/83049258042?pwd=UWViaWNvTFUrdFdhOHJCdEVydnVkdz09
Meeting ID: 830 4925 8042
Passcode: 1729=x3+y3
Speaker: Andre Nies, The University of Auckland
Title: The structure of the class of K-trivial sets
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract:
The K-trivial sets are antirandom in the sense that the initial
segment complexity in terms of prefix-free Kolmogorov complexity K
grows as slowly as possible. Chaitin introduced this notion in
about 1975, and showed that each K-trivial is Turing below the
halting set. Shortly after, Solovay proved that a K-trivial set
can be noncomputable.
In the past two decades, many alternative characterisations
of this class have been found: properties such as being low for K,
low for Martin-Loef (ML) randomness, and a basis for ML randomness,
which state in one way or the other that the set is close to computable.
Initially, the class of noncomputable K-trivials appeared to be
amorphous. More recently, an internal structure has been found.
Most of these results can be phrased in the language of a
reducibility on the K-trivials which is weaker than Turing's:
A is ML-below B if each ML-random computing B also computes A.
Bienvenu, Greenberg, Kucera, Nies and Turetsky (JEMS 2016)
showed that there an ML complete K-trivial set. Greenberg,
Miller and Nies (JML, 2019) established a dense hierarchy of
subclasses of the K-trivials based on fragments of Omega
computing the set, and each such subclass is an initial
segment for ML. More recent results (see arxiv.org/abs/1707.00258,
updated and submitted Dec 2020) generalise these approaches using
cost functions. They also show that each K-trivial set is
ML-equivalent to a c.e. K-trivial.
The extreme lowness of K-trivials, far from being an obstacle,
allows for methods which don't work in a wider setting. The talk
provides an overview and discusses open questions. For instance,
is ML-completeness an arithmetical property of K-trivials?
This is joint work with Noam Greenberg, Joseph Miller and Dan Turetsky
Barcelona Set Theory Seminar
Barcelona Logic Seminar
1/27/2022 15:17:41
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: Rupert McCallum
TITLE: Intrinsic Justifications in Set theory
DATE: 2 February 2022
TIME: 16:00 (CET)
PLACE: The Seminar will take place online via Zoom:
Meeting ID: 985 6524 7347
Passcode: 243408
Best regards,
Joan
P.S.: If you do not wish to receive any more announcements, please send an email to
bagaria@ub.edu with the text “Unsubscribe”.
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
joan.bagaria@icrea.catbagaria@ub.edu
Logic Seminar 26 January 2022 16:00 hrs at NUS by Zhang Jing (today)
NUS Logic Seminar
1/25/2022 18:24:42
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 26 January 2022, 16:00 hrs
Talk via Zoom:
https://nus-sg.zoom.us/j/83049258042?pwd=UWViaWNvTFUrdFdhOHJCdEVydnVkdz09
Meeting ID: 830 4925 8042
Passcode: 1729=x3+y3
Speaker: Zhang Jing
Title: Ramsey-type theorems on large structures
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract:
Structures like trees, linear orders, partial orders, graphs have
been widely studied in different areas of mathematics. The Ramsey-type
theorems we will discuss usually take the following form: for any given
coloring of the structure, there exists a "large sub-structure" that
intersects "very few" color classes. One example is a theorem of Laver that
states for any finite coloring of Q x Q (ordered pairs of rationals), there
exists X, Y order isomorphic to Q, such that X x Y intersects at most 2
color classes. We will discuss the uncountable analogues of these
statements and their consistency. In particular, a diagonal version of the
Halpern-Lauchli theorem plays a key role. The differences between countable
combinatorics and uncountable combinatorics will be highlighted.
Wednesday seminar
Prague Set Theory Seminar
1/24/2022 6:59:12
Dear all,
The seminar meets on Wednesday January 26th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: Jonathan Cancino -- There may be no I-ultrafilter for any
F_sigma ideal I
The notion of I-ultrafilter was introduced by Baumgartner, and it has
been useful in providing a framework for classifying many combinatorial
properties of ultrafilters. In this talk we prove, however, that the
class of F_sigma ideals may provide a vacuous classification of the
combinatorial properties of ultrafilters, that is, F_sigma ideals may be
not useful in providing combinatorial information about ultrafilters.
This in turn implies that consistently there is no Hausdorff
ultrafilter, thus answering a classical question of M. Di Nasso and M.
Forti.
Best,
David
(KGRC) video recording of Víctor Torres's talk
Kurt Godel Research Center
1/21/2022 10:36:49
A recording of the talk of Víctor Torres from January 13th at the KGRC
Logic Colloquium can be found here:
https://univienna.zoom.us/rec/share/c3uO9AKcscJmC_PiuEwwdF_keDWgnGJaXjHykFSUX3pvdT5huEU0BHjw5rFdJdVc.AN_ekNznONDnOZD0
Password: !F8^vg followed by 7j
(KGRC) Logic Colloquium talk on Thursday, January 27
Kurt Godel Research Center
1/20/2022 12:24:22
Logic Colloquium
Kurt Gödel Research Center
Thursday, January 27
"The Banach-Tarski paradox, monsters and their gentler cousins"
Yash Lodha (Uni Wien)
The Banach-Tarski paradox is one of the most striking and counterintuitive
phenomena in all of mathematics. Von Neumann's study of the paradox led to the
formulation of the so called von Neumann-Day problem, which has been attributed
to Mahlon Day from the 1950s. The problem was solved in the late 70s by the
construction of various finitely generated "monster" groups. However, I will
explain how elementary tools from descriptive set theory recently led to the
construction of considerably "less scary" new solutions, some of which are
finitely presented (and even type F_{\infty}).
Time and Place
Talk at 3:00pm via Zoom--if you have not received the meeting link by the
day before the talk, please contact richard.springer@univie.ac.at!
This Week in Logic at CUNY
This Week in Logic at CUNY
1/18/2022 14:08:45
Hi everyone,
Welcome back, and Happy New Year! Note that CUNY's semester begins on January 28th. However, there are some meetings taking place prior to that - see below.
Best,
Jonas
This Week in Logic at CUNY:
- - - - Monday, Jan 17, 2022 - - - -
- - - - Tuesday, Jan 18, 2022 - - - -
- - - - Wednesday, Jan 19, 2022 - - - -
- - - - Thursday, Jan 20, 2022 - - - -
- - - - Friday, Jan 21, 2022 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, January 21, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
Wolfgang Wohofsky, University of Vienna
Distributivity spectrum and fresh functions: Part II
We discuss different notions of a distributivity spectrum of forcings.
In the first talk, I will mainly focus on the notion of fresh functions and the corresponding spectrum. A function with domain lambda is fresh if it is new but all its initial segments are in the ground model. I will give general facts how to compute the fresh function spectrum, also discussing what sets are realizable as a fresh function spectrum of a forcing. Moreover, I will provide several examples, including well-known tree forcings on omega such as Sacks and Mathias forcing, as well as Prikry and Namba forcing to illustrate the difference between fresh functions and fresh subsets.
In the second talk, I will also discuss another ('combinatorial') distributivity spectrum; most importantly, analyzing this notion for the forcing P(omega)/fin.
This is joint work with Vera Fischer and Marlene Koelbing.
Next Week in Logic at CUNY:
- - - - Monday, Jan 24, 2022 - - - -
- - - - Tuesday, Jan 25, 2022 - - - -
- - - - Wednesday, Jan 26, 2022 - - - -
- - - - Thursday, Jan 27, 2022 - - - -
- - - - Friday, Jan 28, 2022 - - - -
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
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jreitz@nylogic.org.
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jreitz@nylogic.org.
(KGRC) Set Theory Seminar talk on Tuesday, January 18
Kurt Godel Research Center
1/13/2022 17:38:27
The KGRC welcomes as guest:
Gunter Fuchs (host: Vera Fischer) will visit the KGRC from January 17 to
January 20 and give a talk (see below).
* * *
Set Theory Research Seminar
Kurt Gödel Research Center
Tuesday, January 18
"Blurry definability"
Gunter Fuchs
(City University of New York, USA)
In this talk on ongoing research, I analyze blurry forms of ordinal
definability and their hereditary versions which generalize ideas due to
Hamkins/Leahy and Tzouvaras. Classically, a set is ordinal definable if it
is the _unique_ object satisfying some first order property in which
ordinal parameters may occur. Given a cardinal kappa, I define that a set
is
Wednesday seminar
Prague Set Theory Seminar
1/13/2022 8:16:40
Dear all,
The seminar meets on Wednesday January 19th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: Chris Lambie-Hanson -- Variations on theorems of Silver and
Galvin-Hajnal
We will begin by reviewing the celebrated theorems of Silver and
Galvin-Hajnal about cardinal exponentiation at singular cardinals of
uncountable cofinality. We will then present some recent variations on
these theorems concerning cardinal characteristics at singular
cardinals, focusing in particular on the dominating number.
Also, there is a small online set theory conference tomorrow (Friday),
see https://www1.maths.leeds.ac.uk/~pmtadb/STUK7/STUK7.html
Best,
David
Logic Seminar Talk 19 Jan 2022 16:00 hrs at NUS over Zoom by Ye Jinhe
NUS Logic Seminar
1/12/2022 18:42:13
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 19 January 2022, 16:00 hrs
Talk via Zoom:
https://nus-sg.zoom.us/j/83049258042?pwd=UWViaWNvTFUrdFdhOHJCdEVydnVkdz09
Meeting ID: 830 4925 8042
Passcode: 1729=x3+y3
Speaker: Ye Jinhe,
Institut de Mathematiques de Jussieu - Paris Rive Gauche
Title: Curve-Excluding Fields
Abstract: Consider the class of fields with Char(K)=0 and x^4+y^4=1
has only 4 solutions in K, we show that this class has a model
companion, which we denote by curve-excluding fields. Curve-excluding
fields provides (counter)examples to various questions. Model
theoretically, they are model complete. Field theoretically, they are
not large and unbounded. Time permitting, we will discuss other
aspects such as decidability of such fields.
Joint work with Will Johnson and Erik Walsberg.
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
World Logic Day Event // January 14
Set Theory Seminar at the Fields Institute
1/9/2022 18:36:42
January 14th is World Logic Day, as designated by the UNSECO, see
On this day the Toronto Set Theory Seminar at the Fields Institute will
hold
a special session with 5 short talks (20 minutes each), showcasing
recent
research by faculty and postdocs at University of Toronto:
====================================================================
Friday January 14 at the Set Theory Seminar (Fields Institute, Toronto):
Location: https://zoom.us/j/92701726800
====================================================================
13:30
Ivan Ongay-Valverde and Franklin D. Tall﹡: A New Topological
Generalization of Descriptive Set Theory
We generalize the K-analytic spaces to the K-σ-projective spaces. We get
an application to Selection Principles:
Theorem. The Axiom of σ-Projective Determinacy implies every
K-σ-projective Menger space is Hurewicz.
--------------------------------------------------------------------
13:50
Ivan Ongay Valverde﹡ and Franklin D. Tall: Upper semi-continuous
compact-valued functions and the K-sigma-projective hierarchy
Completing the previous talk, we introduce USCCV functions (actually,
multifunctions), which were employed in the study of K-analytic spaces,
and show how to use them to prove the crucial:
Theorem. K-σ-projective spaces are projectively σ-projective.
--------------------------------------------------------------------
14:10
Christopher J. Eagle, Clovis Hamel﹡, Sandra Müller, and Franklin D.
Tall: An undecidable extension of Morley's theorem on the number of
countable models
Morley’s theorem states that the number of non-isomorphic countable
models of a complete countable first-order theory in a countable
language is ℵ0 or ℵ1 or 2ℵ0. Vaught’s conjecture remains one of the most
important open problems in Model Theory, asking whether ℵ1 can be
omitted in the conclusion of Morley’s theorem. Even though Vaught’s
conjecture is trivially false in second-order logic, no result was known
regarding Morley’s trichotomy for second-order logic. We shall show
using forcing, large cardinals and descriptive set theory that the
second-order version of Morley’s theorem is undecidable.
--------------------------------------------------------------------
14:30
Andrew Marks and Spencer Unger﹡: Flows on the torus
In joint work with Andrew Marks, we gave a constructive solution to
Tarski's circle squaring problem. In particular, we showed that a disk
and a square with the same area are equidecomposible using translations.
One important innovation of the proof was to construct a real valued
flow from the disk to the square. The notion of flow that we use comes
from the study of networks and is related to max flow-min cut. In this
talk, I will sketch a simpler construction of a real-valued flow from
the disk to the square, which is joint work with Andrew Marks. Using
discrepancy estimates due to Laczkovich, this argument works for sets
whose boundary has small upper Minkowski dimension. I will also mention
ongoing work with Anton Bernshteyn and Anush Tserunyan where we
construct a large and diverse collection of flows under the same
assumptions.
--------------------------------------------------------------------
14:50
Haosui Duanmu, David Schrittesser﹡, and William Weiss: Infinitesimals
and Probabilities
In joint work with Haosui Duanmu and William Weiss, we investigate
applications of nonstandard analysis in measure theory. The use of
infinitesimals and hyperfinite probability spaces offers alternative
viewpoints on many classical problems, via Peter Loeb's construction of
measures using hyperfinite probability mass functions to construct
classical measures. In this talk, I will describe a solution to a
problem posed by Keisler, about Loeb measures, and also mention
applications in statistics which are joint work with Haosui Duanmu and
Daniel Roy.
--------------------------------------------------------------------
Find this program also at:
For more information about events worldwide see also
--
http://homepage.univie.ac.at/david.schrittesser
pronouns he/him
(KGRC) (corrected) World Logic Day 2022
Kurt Godel Research Center
1/6/2022 17:50:16
(Correction: Parts of the most recent announcement gave the wrong begin time
for Victor's talk in the Logic Colloquium. The correct time is 11:30am - apologies
for any confusion caused! Below is the corrected text for the announcement.)
On January 14th is the World Logic Day. The KGRC is making a small contribution
towards the celebrations by dedicating the Tuesday and Thursday seminars next
week to it. For more information about events worldwide see
https://wld.cipsh.international/background.html
* * *
Set Theory Research Seminar
Kurt Gödel Research Center
Tuesday, January 11
The Set Theory Research Seminar will host five short talks given by masters and
doctoral students on topics from their theses. For information regarding the
schedule, titles and abstracts see the attached file (the talks are mainly
intended for a student audience).
Time and Place
Talks at 3:00pm via Zoom - see attached file for schedule. If interested
contact vera.scher@univie.ac.at.
* * *
Logic Colloquium
Kurt Gödel Research Center
Thursday, January 13
"Worlds without Martin's Axiom"
Víctor Torres-Pérez (TU Wien)
The first of Hilbert's famous list of problems at the beginning of the 20th
century was to establish Cantor's Continuum Hypothesis (CH), i.e. if there is
no uncountable subset of the reals with cardinality strictly less than the
continuum. After the works of Gödel and Cohen, it was concluded that the
traditional axioms of Set Theory (ZFC) cannot decide CH.
Since then, new axioms have emerged. Prominently we have Forcing Axioms. One of
the first Forcing Axioms ever considered was Martin's Axiom (MA). While MA
implies the negation of the CH, it does not decide the exact value of the
continuum. However, generalizations of MA like the Proper Forcing Axiom (PFA)
or Martin's Maximum (MM) do imply that the continuum is the second uncountable
cardinal. Besides, PFA or MM imply the negation of certain square principles or
tree properties (among a very large number of interesting consequences). This
means in particular that these axioms require the existence of large cardinals.
There are other relatively new principles, which have strong consequences
similar to the ones from PFA or MM, but they can coexist consistently with the
absence of MA or even imply this absence. A couple of these principles are, for
example, Rado's Conjecture (RC) and the P-Ideal Dichotomy (PID). We will give a
general review of results involving these kinds of principles, including some
of ours obtained along the previous years. There, it is possible to observe
that even if they can avoid MA, they are still quite powerful like these
traditional Forcing Axioms. We will expose one of our last results, where we
prove (with L. Wu) that PID implies the negation of a certain type of
two-cardinals square principle.
Time and Place
Talk at 11:30am via Zoom - Please note the unusual time! If you have not
received the meeting link by the day before the talk, please contact
richard.springer@univie.ac.at!
Tagged: Lukas Koschat, Valentin Haberl, Fabian Kaak, Michał Godziszewski, Lorenzo Sauras, Víctor Torres-Pérez
Logic Day Special Wed 12 Jan 2022 16:00 hrs SGT
NUS Logic Seminar
1/5/2022 9:21:24
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 12 Jan 2022, 16:00 hrs
Talk via Zoom:
https://nus-sg.zoom.us/j/83049258042?pwd=UWViaWNvTFUrdFdhOHJCdEVydnVkdz09
Meeting ID: 830 4925 8042
Passcode: 1729=x3+y3
(1) Logic Day Special
For the logic day, everyone is encouraged to present his or her favourate
result, which is not required to be recent. Alternatively the participant
can also present open questions, perhaps with partial results. Every
contribution is welcome.
For planning purposes, please email contributions to Frank Stephan
(fstephan@comp.nus.edu.sg) and Yang Yue (matyangy@nus.edu.sg).
(2) Planning of Logic Seminar
At http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
you find a schedule of the so far reserved slots. If you are willing to
present a talk in the logic seminar (40 - 50 minutes), please select one day
which is still free and we will note you down. The timing can be changed
if needed.
Also if you happen to know of someone who might be interested in giving
a talk, please inform us and we will follow up with this person.
Frank Stephan (fstephan@comp.nus.edu.sg)
Yang Yue (matyangy@nus.edu.sg)
Organisers of the Logic Seminar
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Wednesday seminar
Prague Set Theory Seminar
1/4/2022 6:37:19
Dear all,
No seminar tomorrow, Wednesday January 5th.
The seminar meets again on Wednesday January 12th at 11:00 in the
Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front
building.
Program: David Uhrik -- Cohen reals and partition relations
Abstract: The effect of adding Cohen reals on partition relations will
be discussed. Specifically, we will prove that the relation omega_2 -->
(omega_2, omega:omega)^2 holds after adding Cohen reals to a model of
CH. We will also prove that this result is in a sense best possible.
Best,
David
21.12.2021 Seminar canceled
IMPAN Working Group in Applications of Set Theory
12/20/2021 13:06:19
Due to health issues of several participants we need to cancel the meeting of the seminar tomorrow 21.12.2021, when Damian Sobota was supposed to speak. We are very sorry. The talk will be postponed for March/April 2022.
Visit our seminar page which may include some future talks at
https://www.impan.pl/~set_theory/Seminar/
----- Em 18 de Dez de 2021, em 13:35, Piotr Koszmider piotr.koszmider@impan.pl escreveu:
| Seminar: Working group in applications of set theory, IMPAN
|
| Tuesday, 21.12.2021, 13.30, room 403
|
| Speaker: Damian Sobota (KGRC, Vienna)
|
| Title: "Measures with the Additive Property and the random forcing"
|
| Abstact: "Let μ be a finitely additive probability measure on ω which vanishes
| on points, that is, μ({n})=0 for every n∈ω. It follows immediately that μ is
| not σ-additive, however it may be almost σ-additive in the following weak
| sense. We say that μ has the Additive Property, (AP) in short, if for every
| sequence (An) of pairwise disjoint subsets of ω there is a subset A such that
| A_n\A is finite for every n∈ω and μ(A)=Σn μ(A_n). Equivalently, for every
| decreasing sequence (A_n) of subsets of ω there is a subset A such that A\A_n
| is finite for every n∈ω and μ(A)=limn μ(A_n). The latter definition implies
| immediately that, e.g., an ultrafilter U on ω is a P-point if and only if the
| one-point measure δ_U has (AP). And similarly as in the case of P-points the
| existence of measures with (AP) is independent of ZFC.
|
| During my talk I will discuss basic properties of (families of) measures with
| (AP) as well as show, at least briefly, that using old ideas of Solovay and
| Kunen one can obtain a non-atomic measure with (AP) in the random model. The
| latter result implies that in this model there exists a ccc P-set in ω*, which
| may be treated as a (weak) partial answer to the question asking whether there
| are P-points in the random model.
|
| This is a joint work with Piotr Borodulin-Nadzieja."
|
|
|
Damian Sobota, Measures with the Additive Property and the random forcing
IMPAN Working Group in Applications of Set Theory
12/18/2021 7:35:27
Seminar: Working group in applications of set theory, IMPAN
Tuesday, 21.12.2021, 13.30, room 403
Speaker: Damian Sobota (KGRC, Vienna)
Title: "Measures with the Additive Property and the random forcing"
Abstact: "Let μ be a finitely additive probability measure on ω which vanishes on points, that is, μ({n})=0 for every n∈ω. It follows immediately that μ is not σ-additive, however it may be almost σ-additive in the following weak sense. We say that μ has the Additive Property, (AP) in short, if for every sequence (An) of pairwise disjoint subsets of ω there is a subset A such that A_n\A is finite for every n∈ω and μ(A)=Σn μ(A_n). Equivalently, for every decreasing sequence (A_n) of subsets of ω there is a subset A such that A\A_n is finite for every n∈ω and μ(A)=limn μ(A_n). The latter definition implies immediately that, e.g., an ultrafilter U on ω is a P-point if and only if the one-point measure δ_U has (AP). And similarly as in the case of P-points the existence of measures with (AP) is independent of ZFC.
During my talk I will discuss basic properties of (families of) measures with (AP) as well as show, at least briefly, that using old ideas of Solovay and Kunen one can obtain a non-atomic measure with (AP) in the random model. The latter result implies that in this model there exists a ccc P-set in ω*, which may be treated as a (weak) partial answer to the question asking whether there are P-points in the random model.
This is a joint work with Piotr Borodulin-Nadzieja."
Visit our seminar page which may include some future talks at
https://www.impan.pl/~set_theory/Seminar/
Wednesday seminar
Prague Set Theory Seminar
12/18/2021 4:17:16
Dear all,
The seminar meets on Wednesday December 22nd at 11:00 in the Institute
of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
We will have Jan Grebik as a guest (speaker).
Best,
David
This Week in Logic at CUNY
This Week in Logic at CUNY
12/12/2021 22:30:00
Hi everyone,
This will be the final mailing of This Week In Logic for the semester - we will resume in early January. Happy Holidays to all!
Jonas
This Week in Logic at CUNY:
- - - - Monday, Dec 13, 2021 - - - -
Models of Peano Arithmetic (MOPA)
Monday, December 13, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
Cezary Cieśliński, University of Warsaw
On the principle of disjunctive correctness
The disjunctive correctness principle (DC) states that a disjunction of arbitrary (possibly nonstandard) length is true if and only if one of its disjuncts is true. On first sight, the principle seems an innocent and natural generalization of the familiar compositional truth axiom for disjunction. However, Ali Enayat and Fedor Pakhomov demonstrated that (DC) has the same strength as Delta_0 induction, hence it produces a non-conservative extension of the background arithmetical theory.
In the presentation the proof of a stronger result will be presented. Let (DC-Elim) be just one direction of (DC), namely, the implication 'if a disjunction is true, then one of it disjuncts is true'. We will show that already (DC-Elim) carries the full strength of Delta_0 induction; moreover, the proof of this fact will be significantly simpler than the original argument of Enayat and Pakhomov.
Logic and Metaphysics Workshop
Date: Monday, December 13th, 4.15-6.15 (NY time)
For meeting information, please sign up for our mailing list at
https://logic.commons.gc.cuny.edu/about/Dolf Rami (Bochum)
Title: Singular existentials and three different kinds of negation
Abstract: In this paper, I will argue for a new semantic analysis of (i) singular existential and (ii) atomic sentences to be able to cover three possible types of negation of them. Firstly, I will show that all three negations of sentences of kind (i) are equivalent if we make use of referring or non-referring names, while on the other hand the three negations of sentences of kind (ii) have several non-equivalent readings if non- referring names are used. Secondly, I will review the partial solutions to our problem given by Russell, Quine and Sainsbury and show in how far they fail. Thirdly, I will propose an alternative solution based on a semantics outlined in Rami (2020). Finally, I will show that we must distinguish two types of negation and that a unification in both directions fails.
- - - - Tuesday, Dec 14, 2021 - - - -
Computational Logic seminar
Tuesday December 14, 2021, 2-4pm, Eastern Time US
Contact
sartemov@gc.cuny.edu for a zoom link
Speaker: V. Alexis Peluce, CUNY Graduate Center
Title: Explicit Modal Logic as the Structure of Relevance
Abstract. Orlov and Gödel pioneered the method of syntactic translation of propositional formulas into modal language. Justification Logic takes this a step further by revealing the explicit content of individual modalities. Sergei Artemov extended Gödel's work by showing that S4 can be interpreted in the Logic of Proofs, which can in turn be interpreted in terms of arithmetical proof predicates, thereby providing a rigorous arithmetical foundation for constructivism.
In this work, we examine Classical Logic through the Gödel-Artemov lens. The paradoxes of material implication are a family of classical implications that diverge in meaning from the natural language conditional. We present seven such paradoxes, translate them into S5|the natural modal counterpart of CPC|and then populate the resulting S5 formulas with explicit modalities. We show that for each of our paradoxes, there is a corresponding explicit, non-paradoxical formula. This, we suggest, provides a general method for solving the paradoxes of material implication.
- - - - Wednesday, Dec 15, 2021 - - - -
The New York City Category Theory Seminar
Department of Computer Science
Department of Mathematics
The Graduate Center of The City University of New York
Speaker: Samantha Jarvis, The CUNY Graduate Center.
Date and Time: Wednesday December 15, 2021, 7:00 - 8:30 PM., on Zoom (contact
noson@sci.brooklyn.cuny.edu for the link)
TBA
- - - - Thursday, Dec 16, 2021 - - - -
- - - - Friday, Dec 17, 2021 - - - -
Next Week in Logic at CUNY:
- - - - Monday, Dec 20, 2021 - - - -
- - - - Tuesday, Dec 21, 2021 - - - -
- - - - Wednesday, Dec 22, 2021 - - - -
- - - - Thursday, Dec 23, 2021 - - - -
- - - - Friday, Dec 24, 2021 - - - -
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to
jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email
jreitz@nylogic.org.
Agnieszka Widz, Magic Sets
IMPAN Working Group in Applications of Set Theory
12/12/2021 6:28:53
Seminar: Working group in applications of set theory, IMPAN
Tuesday, 14.12.2021, 13.30, room 403
Speaker: Agnieszka Widz (Lodz University of Technology)
Title: Magic Sets
Abstact: Given a family of real functions F we say that a set M ⊆ ℝ is magic for F if for all f, g ∈ F we have f [M ] ⊆ g[M ] ⇒ f = g. This notion was introduced by Diamond, Pomerance and Rubel in 1981 [1]. Recently some results about magic sets were proved by Halbeisen, Lischka and Schumacher [2]. Inspired by their work I constructed two families of magic sets one of them being almost disjoint and the other one being independent. During my talk I will sketch the background and present the proof for the independent family, which uses a Kurepa tree.
References:
[1] H. G. Diamond, C. Pomerance, L. Rubel, Sets on which an entire function is determined by its range, Mathematische Zeitschrift, 176 (1981), 383-398.
[2] L. Halbeisen, M. Lischka, S. Schumacher, Magic Sets, Real Anal. Exchange, 43 (2018), 187-204.
Visit our seminar page which may include some future talks at
https://www.impan.pl/~set_theory/Seminar/
Barcelona Set Theory Seminar
Barcelona Logic Seminar
12/11/2021 10:59:43
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: Luca Motto-Ros (Torino)
TITLE: Generalized Polish spaces at reguulart uncountable cardinals
DATE: 15 December 2021
TIME: 16:00 (CET)
PLACE: The Seminar will take place online via Zoom:
Meeting ID: 985 6524 7347
Passcode: 243408
Best regards,
Joan
P.S.: If you do not wish to receive any more announcements, please send an email to
bagaria@ub.edu with the text “Unsubscribe”.
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
joan.bagaria@icrea.catbagaria@ub.edu
Wednesday seminar
Prague Set Theory Seminar
12/10/2021 11:51:26
Dear all,
The seminar meets on Wednesday December 15th at 11:00 in the Institute
of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program; we will have another attempt at:
Adam Bartoš -- KPT correspondence in the context of weak Fraïssé
categories (continued)
Last time we formulated the KPT correspondence theorem in our setting,
and summarized abstract Fraïssé theory in our setting. Next time we
discuss the weak amalgamation property, the (weak) Ramsey property in
the abstract setting, recall extreme amenability, and prove the main
theorem. If time permits, we mention applications for strong trees.
Best,
David
(KGRC) four talks on Tuesday, December 14 and one talk on Thursday, December 16
Kurt Godel Research Center
12/9/2021 12:39:00
Note: Effective December 14, the password for the Set Theory
Research Seminar changes (again); if you have not received
the meeting link(s) by the day before the talk, please contact
richard.springer@univie.ac.at!
* * *
Set Theory Research Seminar
Kurt Gödel Research Center
Tuesday, December 14
The Set Theory Research Seminar on December 14th, 2021 will feature four talks given by doctoral students. Julia
Millhouse and Lukas Schembecker will give 25 minute expository talks on selected topics. Marlene Koelbing and
Yuxin Zhou, who are graduating doctoral students at University of Vienna and University of Florida, respectively,
will give 50 minute presentations on results from their dissertations.
For the schedule of the talks, titles and abstracts, please see the attached file.
The Zoom link and Meeting ID will stay the same, but the password will change.
If there are any questions, please direct them to vera.fischer@univie.ac.at!
* * *
Logic Colloquium
Kurt Gödel Research Center
Thursday, December 16
"Classification of definable quotients"
Martin Hils (Universität Münster, Germany)
In many areas of mathematics, quotient objects play an important role, and it is often useful to close a category
under quotients. In the talk, we will discuss so-called imaginaries, i.e., definable quotients in first order
logic. In algebraically closed and in real closed fields, imaginaries may be eliminated. In valued fields, the
situation is more interesting, as there are definable quotients like the residue field and value group which may
not be eliminated. In algebraically closed valued fields, the imaginaries were classified by
Haskell-Hrushovski-Macpherson. We will discuss a recent generalization of their work to more general henselian
valued fields, which is joint with Silvain Rideau-Kikuchi.
Time and Place
Talk at 3:00pm via Zoom - if you have not received the meeting link by the day before the talk, please contact
richard.springer@univie.ac.at!
Tagged: Julia Millhouse, Lukas Schembecker, Marlene Koelbing, Yuxin Zhou, Martin Hils
Mirna Dzamonja @ Toronto Set Theory Seminar
Set Theory Seminar at the Fields Institute
12/6/2021 11:38:29
This week at the Toronto Set Theory Seminar at the Fields Institute:
-------------------------------------------------------------------
Title: Morass-generic structures
Speaker: Mirna Dzamonja, IRIF (CNRS-Université deParis)
Date and Time: Friday, December 10, 2021 - 13:30 to 15:00 (Toronto
time)
Abstract:
We discuss a joint work with Wiesław Kubiś on a specific way of
constructing structures of size ℵ1 using finite approximations, namely
by organising the approximations along a simplified morass. We
demonstrate a connection with Fraïssé limits and show that the naturally
obtained structure of size ℵ1 is homogeneous. Moreover, this is
preserved under expansions, which leads us to a partial answer to a
question of Bassi and Zucker. We give some examples of interesting
structures constructed, such as the antimetric space of size ℵ1.
Finally, we comment on the situation when one Cohen real is added.
Location: https://zoom.us/j/92701726800
-------------------------------------------------------------------
http://www.fields.utoronto.ca/activities/21-22/set-theory-seminar
This Week in Logic at CUNY
This Week in Logic at CUNY
12/5/2021 22:30:00
This Week in Logic at CUNY:- - - - Monday, Dec 6, 2021 - - - -
Models of Peano Arithmetic (MOPA)
Monday, December 6, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
Bartosz Wcisło, Polish Academy of Sciences
Model theoretic characterizations of truth: Part II
This is joint work (still in progress) with Mateusz Łełyk (who gave the first part of the talk). By an axiomatic theory of truth (for the language of arithmetic, L) we mean a theory in L enriched with a fresh unary predicate T(x) which (extends the elementary arithmetic EA and) proves all sentences of the form (ϕ being a sentence in L) T(ϕ)≡ϕ.
The collection of all sentence of the above form is normally called TB−. It is well known that axiomatic theories of truth have a number of interesting model-theoretic consequences. For example, already relatively weak theories of truth impose recursive saturation, in the sense that the L-reduct of any model of such theory is recursively saturated. To give another example, already TB− imposes elementary equivalence of models, in the sense that whenever (M,T)⊨TB−, (M′,T′)⊨TB−, and (M,T)⊂(M′,T) (the first model is a submodel of the second one), then actually M and M′ are elementarily equivalent. During (both parts) of the talk we investigate which of these properties actually characterize the respective truth theory up to definability. In particular, in the first part of the talk, we prove the following results (we restrict ourselves to theories in a finite language and extending EA):
- Every theory which imposes elementary equivalence defines TB−.
- Every theory which imposes full elementarity defines UTB−.
Additionally, we take a look at the definability relations between axiomatic truth theories and axiomatic theories of definability or skolem functions.
Diderik Batens (Ghent)
Title: Every Logic has its Proper Semantics
Abstract: Many logics are sound and complete with respect to a multiplicity of semantic systems. These assign different sets of models to the logic. It will be shown that a series of problems result if all these semantic systems are on a par. I shall present a method to define a unique ‘proper’ semantics for the members of a huge class of logics, containing all usual deductive logics, and argue (i) that the proper semantics is defined in terms of syntactic criteria and so depends fully on the logic, (ii) that there are philosophical arguments to consider a logic’s proper semantics as natural, for example it correctly describes the ‘situations’ that are possible according to the logic. This solves the problems mentioned previously. Implications for the discussion on inferentialism are obvious. For some logics, the proper semantics coincides with the Henkin semantics. For other logics L, the proper semantics counts more models than the Henkin semantics: moreover, not all Henkin models are maximally L-non-trivial. A small change to the Henkin method has the effect that, for every logic L, the Henkin semantics coincides with the proper semantics.
- - - - Tuesday, Dec 7, 2021 - - - -
- - - - Wednesday, Dec 8, 2021 - - - -
The New York City Category Theory SeminarDepartment of Computer ScienceDepartment of MathematicsThe Graduate Center of The City University of New YorkSpeaker: Jens Hemelaer, University of Antwerp.
Date and Time: Wednesday December 8, 2021, 7:00 - 8:30 PM., on Zoom (contact
noson@sci.brooklyn.cuny.edu for the link)
Title: Toposes of presheaves on a monoid and their points.
Abstract: In 2014, Connes and Consani constructed their Arithmetic Site, with as underlying topos the topos of presheaves on the monoid of nonzero natural numbers under multiplication. One of their surprising results is that the points of this topos are classified by a double quotient of the finite adeles, leading immediately to a link with number theory. Inspired by this, we will consider toposes of presheaves on various monoids, and discuss strategies of calculating their points. The most recent strategies (involving for example étale geometric morphisms and complete spreads) are based on joint work with Morgan Rogers.
- - - - Thursday, Dec 9, 2021 - - - -- - - - Friday, Dec 10, 2021 - - - -
Seminar in Philosophy, Logic and Game
Friday, December 10, 10:30 AM
Speaker: David Ellerman, University of Ljubljana
"What is Information and How to Measure it?"
Abstract: In view of the duality between subsets and quotient sets (= partitions = equivalence relations), the Boolean logic of subsets (usually presented as "propositional" logic) has a dual logic of partitions. The quantitative version of Boolean logic is the Boole-Laplace notion of logical probability. Gian-Carlo Rota held that probability is to subsets as information is to partitions, so the quantitative version of partition logic is the theory of logical entropy. This talk is an introduction to logical entropy as the natural measure (in the sense of measure theory) of information as distinctions. It is also shown that the Shannon entropy (which is not a measure) is a uniform transform of logical entropy that is a different quantification of the same notion of information as distinctions.
Set Theory Seminar
CUNY Graduate Center, Room 6417
Friday, December 10, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
Eyal Kaplan, Tel Aviv University
Non-stationary support iterations of Prikry forcings and restrictions of ultrapower embeddings to the ground model, part II
Assume that P is a forcing notion, G is a generic set for it over the ground model V, and a cardinal κ is measurable in the generic extension. Let j be an ultrapower embedding, taken in V[G] with a normal measure on κ. We consider the following questions:
1. Is the restriction of j to V an iterated ultrapower of V (by its measures or extenders)?
2. Is the restriction of j to V definable in V?
By a work of Schindler [1], the answer to the first question is affirmative, assuming that there is no inner model with a Woodin Cardinal and V=K is the core model. By a work of Hamkins [2], the answer to the second question is positive for forcing notions which admit a Gap below κ.
We will address the above questions in the context of nonstationary-support iteration of Prikry forcings below a measurable cardinal κ. Assuming GCH only in the ground model, we provide a positive answer for the first question, and describe in detail the structure of j restricted to V as an iteration of V. The answer to the second question may go either way, depending on the choice of the measures used in the Prikry forcings along the iteration; we will provide a simple sufficient condition for the positive answer. This is a joint work with Moti Gitik.
[1] Ralf Schindler. Iterates of the core model. Journal of Symbolic Logic, pages 241–251, 2006.
[2] Joel David Hamkins. Gap forcing. Israel Journal of Mathematics, 125(1):237–252, 2001.
Next Week in Logic at CUNY:
- - - - Monday, Dec 13, 2021 - - - -
Models of Peano Arithmetic (MOPA)
Monday, December 6, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
Cezary Cieśliński, University of Warsaw
On the principle of disjunctive correctness
The disjunctive correctness principle (DC) states that a disjunction of arbitrary (possibly nonstandard) length is true if and only if one of its disjuncts is true. On first sight, the principle seems an innocent and natural generalization of the familiar compositional truth axiom for disjunction. However, Ali Enayat and Fedor Pakhomov demonstrated that (DC) has the same strength as Delta_0 induction, hence it produces a non-conservative extension of the background arithmetical theory.
In the presentation the proof of a stronger result will be presented. Let (DC-Elim) be just one direction of (DC), namely, the implication 'if a disjunction is true, then one of it disjuncts is true'. We will show that already (DC-Elim) carries the full strength of Delta_0 induction; moreover, the proof of this fact will be significantly simpler than the original argument of Enayat and Pakhomov.
Logic and Metaphysics Workshop
Date: Monday, December 13th, 4.15-6.15 (NY time)
For meeting information, please sign up for our mailing list at
https://logic.commons.gc.cuny.edu/about/Dolf Rami (Bochum)
Title: Singular existentials and three different kinds of negation
Abstract: In this paper, I will argue for a new semantic analysis of (i) singular existential and (ii) atomic sentences to be able to cover three possible types of negation of them. Firstly, I will show that all three negations of sentences of kind (i) are equivalent if we make use of referring or non-referring names, while on the other hand the three negations of sentences of kind (ii) have several non-equivalent readings if non- referring names are used. Secondly, I will review the partial solutions to our problem given by Russell, Quine and Sainsbury and show in how far they fail. Thirdly, I will propose an alternative solution based on a semantics outlined in Rami (2020). Finally, I will show that we must distinguish two types of negation and that a unification in both directions fails.
- - - - Tuesday, Dec 14, 2021 - - - -
- - - - Wednesday, Dec 15, 2021 - - - -
The New York City Category Theory Seminar
Department of Computer Science
Department of Mathematics
The Graduate Center of The City University of New York
Speaker: Samantha Jarvis, The CUNY Graduate Center.
Date and Time: Wednesday December 15, 2021, 7:00 - 8:30 PM., on Zoom (contact
noson@sci.brooklyn.cuny.edu for the link)
TBA
- - - - Thursday, Dec 16, 2021 - - - -
- - - - Friday, Dec 17, 2021 - - - -
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to
jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email
jreitz@nylogic.org.
Kacper Kucharski, Overcomplete sets in selected nonseparable Banach spaces
IMPAN Working Group in Applications of Set Theory
12/4/2021 14:54:33
Seminar: Working group in applications of set theory, IMPAN
Tuesday, 7.12.2021, 13.30, room 403
Speaker: Kacper Kucharski (UW)
Title: "Overcomplete sets in selected nonseparable Banach spaces"
Abstact: "A subset Y of a Banach space X is called overcomplete if |Y|=dens(X) and for any set Z⊆Y, such that |Z|=|Y|, Z is linearly dense in X. A classical result says that every separable Banach space admits an overcomplete set. The main goal of the talk is to show how, using a certain Aronszajn tree, one can step-up this property for selected nonseparable Banach spaces. If there is enough time, one consistency result will also be stated and proved".
Visit our seminar page which may include some future talks at
https://www.impan.pl/~set_theory/Seminar/
Barcelona Set Theory Seminar
Barcelona Logic Seminar
12/4/2021 5:50:46
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: Philipp Schlicht (Bristol)
TITLE: Forcing axioms via ground model interpretations
DATE: 8 December 2021
TIME: 16:00 (CET)
PLACE: The Seminar will take place online via Zoom:
Meeting ID: 985 6524 7347
Passcode: 243408
Best regards,
Joan
P.S.: If you do not wish to receive any more announcements, please send an email to
bagaria@ub.edu with the text “Unsubscribe”.
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
joan.bagaria@icrea.catbagaria@ub.edu
Wednesday seminar
Prague Set Theory Seminar
12/3/2021 6:30:22
Dear all,
Because of an increasing number of covid infections among regular
seminar participants, the seminar next week, Wednesday December 8th is
cancelled.
It is unclear whether the seminar will resume in December, no
announcement = no seminar.
The expected program for the next seminar is Adam Bartoš finishing his
talk on KPT correspondence in the context of weak Fraïssé categories.
(This week we had a talk by Chris Lambie-Hanson instead.)
Moreover, there are some sad news from Kosice, see attachment.
Best,
David
(KGRC) Set Theory Research Seminar talk on Tuesday, December 7
Kurt Godel Research Center
12/2/2021 15:16:47
Note: The KGRC Set Theory Seminar recently moved to another Zoom meeting
(while other KGRC events kept their Zoom meetings). If you have not
received the meeting link by the day before the talk, please contact
richard.springer@univie.ac.at!
(Please direct any other requests pertaining to the Set Theory Seminar and
its Zoom meeting to vera.fischer@univie.ac.at.)
* * *
Set Theory Research Seminar
Kurt Gödel Research Center
Tuesday, December 7
"On regular countably compact R-rigid spaces"
Serhii Bardyla (KGRC)
A regular separable first-countable countably compact space is called a Nyikos
space. A space $X$ is called R-rigid if any continuous real-valued function on
$X$ is constant. Under MA we construct an R-rigid Nyikos space. This way we
answer a few questions of Tzannes and extend results of Ciesielski and
Wojciechowski.
This is a joint work with Zdomskyy.
Time and Place
Talk at 3:00pm via Zoom - see top of this message
Mariam Beriashvili @ Toronto Set Theory Seminar // UNUSUAL TIME
Set Theory Seminar at the Fields Institute
11/30/2021 2:14:27
This week at the Toronto Set Theory Seminar at the Fields Institute:
-------------------------------------------------------------------
Title: On two-point sets and other nontrivial point sets
Speaker: Mariam Beriashvili, I. Vekua Institute of Applied Mathematics,
Iv. Javakhishvili Tbilisi State University, Tbilisi, Georgia
Date and Time: Friday, December 3, 2021 - 10:00am to 11:30am
Abstract:
We consider certain pathological point sets from the general measure
theoretical point of view. Namely, we discuss Mazurkiewicz sets, also
called two-point sets, which have difficult and interesting descriptive
as well as measure theoretic properties. Moreover, we will discuss also
uniform subsets of the Euclidean space and their connections to the
Mazurkiewizc sets. Also, in the talk will be considered Bernstein sets
and Hamel bases.
Location: https://zoom.us/j/92701726800
-------------------------------------------------------------------
http://www.fields.utoronto.ca/activities/21-22/set-theory-seminar
Mariam Beriashvili @ Toronto Set Theory Seminar // UNUSUAL TIME
Set Theory Seminar at the Fields Institute
11/30/2021 2:14:59
This week at the Toronto Set Theory Seminar at the Fields Institute:
-------------------------------------------------------------------
Title: On two-point sets and other nontrivial point sets
Speaker: Mariam Beriashvili, I. Vekua Institute of Applied Mathematics,
Iv. Javakhishvili Tbilisi State University, Tbilisi, Georgia
Date and Time: Friday, December 3, 2021 - 10:00am to 11:30am
Abstract:
We consider certain pathological point sets from the general measure
theoretical point of view. Namely, we discuss Mazurkiewicz sets, also
called two-point sets, which have difficult and interesting descriptive
as well as measure theoretic properties. Moreover, we will discuss also
uniform subsets of the Euclidean space and their connections to the
Mazurkiewizc sets. Also, in the talk will be considered Bernstein sets
and Hamel bases.
Location: https://zoom.us/j/92701726800
-------------------------------------------------------------------
http://www.fields.utoronto.ca/activities/21-22/set-theory-seminar
Barcelona Set Theory Seminar
Barcelona Logic Seminar
11/28/2021 12:48:06
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: Menachem Magidor (Jerusalem)
TITLE: Borel canonization of analytic and universally Baire relations
DATE: 1 December 2021
TIME: 16:00 (CET)
PLACE: The Seminar will take place online via Zoom:
Meeting ID: 985 6524 7347
Passcode: 243408
Best regards,
Joan
P.S.: If you do not wish to receive any more announcements, please send an email to
bagaria@ub.edu with the text “Unsubscribe”.
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
joan.bagaria@icrea.catbagaria@ub.edu
Piotr Koszmider, Bidiscrete system in compact spaces
IMPAN Working Group in Applications of Set Theory
11/27/2021 9:54:46
Seminar: Working group in applications of set theory, IMPAN
Tuesday, 30.11.2021, 13.30, room 403
Speaker: Piotr Koszmider (IM PAN)
Title: "Bidiscrete system in compact spaces"
Abstact: "A set X of the square of a compact Hausdorff space K is called bidiscrete if for every (x, y) in X there is a continuous real valued function f on K such that f(x)=1, f(y)=0 and f(x')=f(y') for any (x', y') in X-{(x, y)}. Bidiscrete sets play role in investigations related to biorthogonal systems in Banach spaces and irredundant sets in many algebraic structures induced by the compact K, but the question if there is in ZFC a nonmetrizable compact K with no uncountable bidiscrete set remains open. There are such examples under special set-theoretic assumptions (Kunen) and there are no such totally disconnected examples under other assumptions (Todorcevic). We will discuss these and other know results and open problems.".
Visit our seminar page which may include some future talks at
https://www.impan.pl/~set_theory/Seminar/
(KGRC) seminar talks on Tuesday, November 30 and Thursday, December 2
Kurt Godel Research Center
11/25/2021 15:57:54
Note: Starting November 30, the Zoom meeting ID and passcode change for
the Set Theory Seminar (but remain unchanged for other KGRC seminars). If
you have not received the meeting link(s) by the day before the talk,
please contact richard.springer@univie.ac.at!
(Please direct any other requests pertaining to the Set Theory Seminar and
its Zoom meeting to vera.fischer@univie.ac.at.)
* * *
Set Theory Research Seminar
Kurt Gödel Research Center
Tuesday, November 30
"Big Ramsey degrees of 3-uniform hypergraphs are finite, part 2"
David Chodounský (TU Wien)
This is a continuation of the KGRC Set Theory seminar talk I gave in June
2021. I will quickly repeat the content of the first talk and focus on
things I did not cover then. It is well known that the (universal
countable) Rado graph has finite big Ramsey degrees. I.e., given a finite
colouring of n-tuples of its vertices there is a copy of the Rado graph
such that its n-tuples have at most D(n)-many colours. The proof of this
fact uses a theorem of Milliken for trees. I will talk about the extension
of this argument which works also for universal structures with higher
arities, in particular 3-uniform hypergraphs.
Joint work with M. Balko, J. Hubička, M. Konečný, and L. Vena, see
https://arxiv.org/abs/2008.00268
Time and Place
Talk at 3:00pm via Zoom - see top of this message
* * *
Logic Colloquium
Kurt Gödel Research Center
Thursday, December 2
"The world between aleph1 and continuum:
from Martin's Axiom to Cichoń's Maximum"
Martin Goldstern (TU Wien)
Georg Cantor's "Continuum Hypothesis" (CH) postulates that the continuum
(the cardinality of the set of real numbers) is equal to aleph1, the
smallest uncountable cardinal. Martin's Axiom (MA) is a weakening of CH;
it implies that all infinite cardinals below the continuum are similar to
aleph0, the cardinality of a countable set. For example, MA implies that
not only every countable union of null (measure zero) sets is still null,
but even every union of fewer than continuum many such sets. This
motivates the definition of a so-called cardinal characteristic, the
additivity number of the measure zero sets - the answer to the question
"how many null sets do we have to join together to get a non-null set".
There is a whole zoo of such cardinal characteristics (some of them
defined long before the advent of forcing); whenever you know that any
countable set of objects with property X will never have property Y, you
may ask how many such objects you need to get to Y.
Accepting CH or just MA as an axiom gives a picture that is on the one
hand very clean, but on the other hand also rather poor: most cardinal
characteristics can then be shown to be equal to the continuum.
In my talk I will discuss - or at least hint at - some recent (and some
old) techniques for constructing "anti-MA" universes, where many cardinals
between omega1 and the continuum appear as cardinal characteristics
(defined by some natural properties X and Y).
I will try to hide all technical details, so that my talk will hopefully
be understandable also for non-set-theorists.
Time and Place
Talk at 3:00pm via Zoom - see top of this message
Wednesday seminar
Prague Set Theory Seminar
11/25/2021 5:59:07
Dear all,
The seminar meets on Wednesday December 1st at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program:
Adam Bartoš will continue his talk from this week.
KPT correspondence in the context of weak Fraïssé categories (continued)
Last time we formulated the KPT correspondence theorem in our setting,
and summarized abstract Fraïssé theory in our setting. Next time we
discuss the weak amalgamation property, the (weak) Ramsey property in
the abstract setting, recall extreme amenability, and prove the main
theorem. If time permits, we mention applications for strong trees.
Best,
David
Toronto Set Theory Seminar
Set Theory Seminar at the Fields Institute
11/23/2021 22:06:27
This week at the Toronto Set Theory Seminar at the Fields Institute:
-------------------------------------------------------------------
Speaker:
David Aspero, University of East Anglia
Date and Time:
Friday, November 26, 2021 - 1:30pm to 2:30pm
Location:
https://zoom.us/j/92701726800
Abstract:
I aim to present the proof that the ℙmax
axiom (*) is implied by Martin's Maximum++, as well as some further work
related to this result and its proof.
-------------------------------------------------------------------
http://www.fields.utoronto.ca/activities/21-22/set-theory-seminar
Barcelona Set Theory Seminar
Barcelona Logic Seminar
11/22/2021 2:50:37
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: Chris Scambler (New York University)
TITLE: Axiomatic Potentialism
DATE: 24 November 2021
TIME: 16:00 (CET)
PLACE: The Seminar will take place online via Zoom:
Meeting ID: 985 6524 7347
Passcode: 243408
Best regards,
Joan
P.S.: If you do not wish to receive any more announcements, please send an email to
bagaria@ub.edu with the text “Unsubscribe”.
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
joan.bagaria@icrea.catbagaria@ub.edu
Kamil Ryduchowski; A Banach space admitting few operators
IMPAN Working Group in Applications of Set Theory
11/21/2021 7:45:24
Seminar: Working group in applications of set theory, IMPAN
Tuesday, 23.11.2021, 13.30, room 403, (CHANGE OF THE ROOM!)
Speaker: Kamil Ryduchowski (MIM UW)
Title: "A Banach space admitting few operators"
Abstact: "Using the colouring discussed in our previous talk we will construct a Banach space admitting few operators in the following sense: it will be a non-separable Banach space X such that every operator on X is of the form sI + S, where s is a scalar, S is an operator with a separable range and I stands for the identity on X, i.e. every operator on X is a homothety modulo the ideal of operators with separable range. The construction is due to Shelah and Steprans".
Visit our seminar page which may include some future talks at
https://www.impan.pl/~set_theory/Seminar/
(KGRC) Set Theory Research Seminar talk on Tuesday, November 23
Kurt Godel Research Center
11/18/2021 17:18:12
Set Theory Research Seminar
Kurt Gödel Research Center
Tuesday, November 23
"Specializing Triples and Weak Embeddability"
Rahman Mohammadpour (TU Wien)
A weak embedding between trees is a function that preserves the strict order. A
class U of trees is said to be universal for a class C of trees if every tree
in C weakly embeds in an element of U. It turns out that the pre-ordered
structure induced by weak embeddability on a class C of trees is a plausible
tool for the study of the elements of C. One can ask e.g., what is the
universality number of a class of trees (the size of the smallest subclass
which is universal)? can it be 1? whether a subclass is cofinal? etc. If CH
holds, then the class of \aleph_1-wide Aronszan trees (trees of height and size
\aleph_1 without cofinal branches) does not have a maximal tree under weak
embeddability (this follows from Kurepa's works). Todorcevic has proved, among
other things, that under MA_{\aleph_1}, the class of Aronszajn trees has no
maximal object. In their joint work on wide Aronszajn trees under
MA_{\aleph_1}, Dzamonja and Shelah introduced the notion of a specializing
triple that connects weak embeddings to the specialization of trees. In
particular, they reproved Todorcevic's result using specializing triples. In
this talk, we shall focus on a variant of this notion in a general setting and
demonstrate the main aspects of it. We shall then discuss some negative results
on the universality problem for Aronszajn trees whose height is the successor
of a regular cardinal, and hopefully, we shall finish the talk with some open
problems.
The results have been obtained in a collaboration with Mirna Dzamonja.
Time and Place
Talk at 3:00pm, mixed mode (in person as well as via Zoom)
Universität Wien
Institut für Mathematik
Lecture Hall HS 8
1st floor
Oskar-Morgenstern-Platz 1
1090 Wien
If you want to attend in person, please be aware of the fact that you will be
required to show proof of your COVID-19 "2.5G" status (vaccinated, recovered,
PCR tested) upon entry of the buildings, or during sporadic random checks in
the seminar rooms. During the lectures we will also pass around an attendance
sheet to facilitate contact tracing. (According to the regulations, this form
will be kept for 28 days and destroyed thereafter.) COVID rules may be
accentuated as prompted by the authorities or the university.
Zoom: This talk will be given in person as well as via Zoom. If you have
not received the meeting link by the day before the talk, please contact
richard.springer@univie.ac.at!
Wednesday seminar
Prague Set Theory Seminar
11/16/2021 5:12:40
Dear all,
There is no seminar tomorrow, Wednesday November 17th (state holiday).
The seminar meets again on Wednesday November 24th at 11:00 in the
Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front
building.
Program: Adam Bartoš -- KPT correspondence in the context of weak
Fraïssé categories
The Kechris–Pestov–Todorčević correspondence states that a Fraïssé class
of first-order structures has the Ramsey property if and only if the
automorphism group of the Fraïssé limit is extremely amenable. We extend
this correspondence to weak Fraïssé categories. This is a joint paper
with Tristan Bice, Keegan Dasilva Barbosa, and Wiesław Kubiś
(https://arxiv.org/abs/2110.01694). At the talk I will give a conceptual
overview of the framework, present main ideas of the proofs, and if time
permits, give examples in the realm of strong trees.
Best,
David
Toronto Set Theory Seminar
Set Theory Seminar at the Fields Institute
11/15/2021 18:32:43
This week at the Toronto Set Theory Seminar at the Fields Institute:
-------------------------------------------------------------------
Speaker:
Mohammad Golshani, IPM
Date and Time:
Friday, November 19, 2021 - 1:30pm to 2:30pm
Location:
https://zoom.us/j/92701726800
Abstract:
I will discuss some recent joint projects with Saharon Shelah about the
relation between ultraproducts and the continuum hypothesis. In
particular, we show that the Keisler's isomorphism theorem implies the
continuum hypothesis, and then prove some consistency results in the
absence of the continuum hypothesis.
-------------------------------------------------------------------
http://www.fields.utoronto.ca/activities/21-22/set-theory-seminar
This Week in Logic at CUNY
This Week in Logic at CUNY
11/14/2021 20:53:52
This Week in Logic at CUNY:
- - - - Monday, Nov 15, 2021 - - - -
Models of Peano Arithmetic (MOPA)
Monday, November 15th, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
Rasmus Blanck, University of Gothenburg
Incompleteness results for arithmetically definable extensions of strong fragments of PA
In this talk, I will present generalisations of some incompleteness results along two axes: r.e. theories are replaced by Σn+1-definable ones, and the base theory is pushed down as far as it will go below PA. Such results are often easy to prove from suitably formulated generalisations of facts used in the original proofs. I will present a handful of such facts, including versions of the arithmetised completeness theorem and the Orey–Hájek characterisation, to show what additional assumptions our theories must satisfy for the results to generalise. Two salient classes of theories emerge in this context: (a) Σn-sound extensions of IΣn + exp, and (b) Πn-complete, consistent extensions of IΣn+1. Finally, I will discuss some results that fail to generalise to Σn+1-definable theories, as well as an open problem related to Woodin's theorem on the universal algorithm.
The presentation is based on the following paper: https://doi.org/10.1017/S1755020321000307
Logic and Metaphysics Workshop
Date: Tomorrow, Monday, November 15th, 4.15-6.15 (NY time)
Speaker: Sara Uckelman (Durham)
Title: John Eliot’s Logick Primer: A bilingual English-Algonquian logic textbook
Abstract: In 1672 John Eliot, English Puritan educator and missionary, published The Logick Primer: Some Logical Notions to initiate the INDIANS in the knowledge of the Rule of Reason; and to know how to make use thereof [1]. This roughly 80 page pamphlet focuses on introducing basic syllogistic vocabulary and reasoning so that syllogisms can be created from texts in the Psalms, the gospels, and other New Testament books. The use of logic for proselytizing purposes is not distinctive: What is distinctive about Eliot’s book is that it is bilingual, written in both English and Massachusett, an Algonquian language spoken in eastern coastal and southeastern Massachusetts. It is one of the earliest bilingual logic textbooks, it is the only textbook that I know of in an indigenous American language, and it is one of the earliest printed attestations of the Massachusett language. In this talk, I will: (1) Introduce John Eliot and the linguistic context he was working in; (2) Introduce the contents of the Logick Primer—vocabulary, inference patterns, and applications; (3) Discuss notions of “Puritan” logic that inform this primer; (4) Talk about the importance of his work in documenting and expanding the Massachusett language and the problems that accompany his colonial approach to this work.
[1] J.[ohn] E.[liot]. The Logick Primer: Some Logical Notions to initiate the INDIANS in the knowledge of the Rule of Reason; and to know how to make use thereof. Printed by M. J., 1672.
- - - - Tuesday, Nov 16, 2021 - - - -
Computational Logic Seminar
Tuesday November 16, 2021, 2-4pm, Eastern Time US
For a zoom link, contact Sergei Artemov (
sartemov@gc.cuny.edu)
Speaker: Alessandra Palmigiano, Vrije Universiteit Amsterdam
Title: Non-distributive logics: from semantics to meaning.
Abstract: The term ‘non-distributive logics’ refers to the wide family of non-classical propositional logics in which the distributive laws α ∧(β ∨γ) ⊢ (α ∧β)∨(α ∧γ) and (α ∨β)∧(α ∨γ) ⊢ α ∨(β ∧γ) do not need to be valid. Since the rise of very well known instances such as quantum logic, interest in non-distributive logics has been building steadily over the years, motivated by insights from a range of fields in logic and neighbouring disciplines. Techniques and ideas have come from pure mathematical areas such as lattice theory, duality and representation, and areas in mathematical logic such as algebraic proof theory, but also from the philosophical and formal foundations of quantum physics, philosophical logic, theoretical computer science, and formal linguistics.
We will discuss an ongoing line of research in the relational (non topological) semantics of non-distributive logics, which is technically rooted in duality and (generalized) correspondence theory.
Not dissimilarly from the conceptual contribution of Kripke frames to the intuitive understanding of modal logics in various signatures, the relational semantics of non-distributive logics can help to illuminate the intuitive meaning of non-distributive logics at a more fundamental and conceptual level.
We discuss the application of the dual characterization methodology to introduce two relational semantic frameworks for non-distributive logics: the polarity-based frames and the graph-based frames. Despite their common root, polarity-based and graph-based semantics give rise to two radically different intuitive interpretations of non-distributive logics: namely, the polarity-based semantics supports the interpretation of non-distributive logics as logics of categories and formal concepts; the graph-based semantics supports a view of non-distributive logics as hyper-constructivist logics, i.e. logics in which the principle of excluded middle fails at the meta-linguistic level (in the sense that, at states in graph-based models, formulas can be satisfied, refuted or neither), and hence their propositional base generalizes intuitionistic logic in the same way in which intuitionistic logic generalizes classical logic. Consequently, we will argue that graph-based semantics supports the interpretation of non-distributive logics as logics of evidential reasoning.
- - - - Wednesday, Nov 17, 2021 - - - -
The New York City Category Theory Seminar
Department of Computer Science
Department of Mathematics
The Graduate Center of The City University of New York
Time: Wednesdays 07:00 PM Eastern Time (US and Canada)
Speaker: Marco Schorlemmer, Spanish National Research Council.
- - - - Thursday, Nov 18, 2021 - - - -
- - - - Friday, Nov 19, 2021 - - - -
Set Theory Seminar
CUNY Graduate Center, Room 6417
Friday, November 19, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
Corey Switzer, University of Vienna
Definable Well Orders and Other Beautiful Pathologies
Many sets of reals - well orders of the reals, MAD families, ultrafilters on omega etc - only necessarily exist under the axiom of choice. As such, it has been a perennial topic in descriptive set theory to try to understand when, if ever, such sets can be of low definitional complexity. Large cardinals rule out such the existence of projective well orders, MAD families etc while it's known that if V=L (or even just 'every real is constructible') then there is a Δ12 well order of the reals and Π11 witnesses to many other extremal sets of reals such as MAD families and ultrafilter bases. Recently a lot of work on the border of combinatorial and descriptive set theory has focused on considering what happens to the definitional complexity of such sets in models in which the reals have a richer structure - for instance when CH fails and various inequalities between cardinal characteristics is achieved. In this talk I will present a recent advance in this area by exhibiting a model where the continuum is ℵ2, there is a Δ13 well order of the reals, and a Π11 MAD family, a Π11 ultrafilter base for a P-point, and a Π11 maximal independent family, all of size ℵ1. These complexities are best possible for both the type of object and the cardinality hence this may be seen as a maximal model of 'minimal complexity witnesses'. This is joint work with Jeffrey Bergfalk and Vera Fischer.
Next Week in Logic at CUNY:
- - - - Monday, Nov 22, 2021 - - - -
Models of Peano Arithmetic (MOPA)
Monday, November 22th, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
Mauro di Nasso, Università di Pisa
Nonstandard natural numbers in arithmetic Ramsey Theory and topological dynamics
The use of nonstandard models *N of the natural numbers has recently found several applications in arithmetic Ramsey theory. The basic observation is that every infinite number in *N corresponds to an ultrafilter on N, and the algebra of ultrafilters is a really powerful tool in this field. Note that this notion also makes sense in any model of PA, where one can consider the 1-type of any infinite number.
Furthermore, nonstandard natural numbers are endowed with a natural compact topology, and one can apply the methods of topological dynamics considering the shift operator x↦x+1 . This very peculiar dynamic has interesting characteristics.
In this talk I will also present a new result in the style of Hindman’s Theorem about the existence of infinite monochromatic configurations in any finite coloring of the natural numbers. A typical example is the following monochromatic pattern:
a, b, c, … , a+b+ab, a+c+ac, b+c+bc, … , a+b+c+ab+ac+bc+abc.
Logic and Metaphysics Workshop
Date: Tomorrow, Monday, November 22th, 4.15-6.15 (NY time)
For meeting information, please sign up for our mailing list at
https://logic.commons.gc.cuny.edu/about/Konstantinos Georgatos (John Jay).
Title: Similarity through indistinguishability: the geodesic reasoning on Kripke models
Abstract: Several logical operators, such as conditionals, revision, and merge, are often understood through the selection of most similar worlds. In applications, similarity is expressed with distance and “most similar” translates to “closest” using a distance metric. We shall argue that similarity may arise through an indistinguishability relation between possible worlds and employ the geodesic distance of such a model to measure closeness. This understanding allows us to define a variety of operators that correspond to merging and revising. I will present a few systems and representation results and will show that revision, merging, and conditioning are interdefinable thus, in effect, satisfying the Ramsey test.
- - - - Tuesday, Nov 23, 2021 - - - -
- - - - Wednesday, Nov 24, 2021 - - - -
- - - - Thursday, Nov 25, 2021 - - - -
- - - - Friday, Nov 26, 2021 - - - -
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
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jreitz@nylogic.org.
Kamil Ryduchowski; An antiramsey coloring of pairs
IMPAN Working Group in Applications of Set Theory
11/13/2021 12:37:59
Seminar: Working group in applications of set theory, IMPAN
Tuesday, 16.11.2021, 13.30, room 105,
Speaker: Kamil Ryduchowski (MIM UW)
Title: "An antiramsey coloring of pairs "
Abstact: "We present a fundamental theorem by Todorcevic, stating that there exists a coloring of the complete graph of the first uncountable cardinality in uncountably many colors without an uncountable monochromatic clique. We also discuss other results of Todorcevic of similar nature, which are in some sense multidimensional variants of that coloring".
Visit our seminar page which may include some future talks at
https://www.impan.pl/~set_theory/Seminar/
(KGRC) seminar talks Tuesday, November 16 and Thursday, November 18
Kurt Godel Research Center
11/11/2021 13:13:40
The KGRC welcomes as guest:
Radek Honzik (host: Vera Fischer) will visit the KGRC from November 14 to
November 19 and give two talks (see below).
* * *
Set Theory Research Seminar
Kurt Gödel Research Center
Tuesday, November 16
"Indestructibility of some compactness principles over models of PFA"
Radek Honzik
(Charles University in Prague, Czech Republic)
Recall that the tree property at a regular cardinal kappa says that every
kappa-tree has a cofinal branch, and the weak Kurepa hypothesis at kappa says
that there exists a tree of size and height kappa which has at least kappa^+
cofinal branches. We will prove that over any transitive model of PFA, the tree
property at omega_2 cannot be destroyed by the single Cohen forcing
Add(omega,1) and the negation of the weak Kurepa hypothesis at omega_1 cannot
be destroyed by a sigma-centered forcing.
We will observe that a model-theoretic principle, Guessing model property
(GMP), is enough for the preservation results. GMP can be formulated also for
larger cardinals. We will give an application of our result by showing that
there is a model in which the negation of the weak Kurepa hypothesis holds at
aleph_{omega+1}.
Time and Place
Talk at 3:00pm, mixed mode (in person as well as via Zoom)
Universität Wien
Institut für Mathematik
Lecture Hall HS 8
1st floor
Oskar-Morgenstern-Platz 1
1090 Wien
If you want to attend in person, please be aware of the fact that you will be
required to show proof of your COVID-19 "2.5G" status (vaccinated, recovered,
PCR tested) upon entry of the buildings, or during sporadic random checks in
the seminar rooms. During the lectures we will also pass around an attendance
sheet to facilitate contact tracing. (According to the regulations, this form
will be kept for 28 days and destroyed thereafter.)
Zoom: This talk will be given in person as well as via Zoom. If you have
not received the meeting link by the day before the talk, please contact
richard.springer@univie.ac.at!
* * *
Logic Colloquium
Kurt Gödel Research Center
Thursday, November 18
"Compactness at small uncountable cardinals"
Radek Honzik
(Charles University in Prague, Czech Republic)
We will discuss various compactness principles such as stationary reflection,
the tree property or Rado conjecture at small cardinals (for instance omega_2).
We will give context and motivation for the principles and discuss and compare
the main sources of these principles: large cardinals and consequences of
forcing axioms. We will focus on indestructibility of these principles with
respect to classes of forcing notions, and give some examples (for instance we
show that stationary reflection at omega_2 cannot be destroyed by a ccc
forcing). Indestructibility is important for investigating connections between
compactness and other areas of set theory such as generalized cardinal
invariants, and we will mention some applications.
Time and Place
Talk at 3:00pm, mixed mode (in person as well as via Zoom)
Universität Wien
Institut für Mathematik
Lecture Hall HS 13
2nd floor
Oskar-Morgenstern-Platz 1
1090 Wien
If you want to attend in person, please be aware of the fact that you will be
required to show proof of your COVID-19 "2.5G" status (vaccinated, recovered,
PCR tested) upon entry of the buildings, or during sporadic random checks in
the seminar rooms. During the talk we will also pass around an attendance sheet
to facilitate contact tracing. (According to the regulations, this form will be
kept for 28 days and destroyed thereafter.)
Zoom: This talk will be given in person as well as via Zoom. If you have
not received the meeting link by the day before the talk, please contact
richard.springer@univie.ac.at!
Two talks next Tuesday
Carnegie Mellon Logic Seminar
11/9/2021 22:56:04
TUESDAY, November 16, 2021
Mathematical logic seminar: 3:30 P.M., Online, William Chan, Carnegie
Mellon University
Zoom link:
https://cmu.zoom.us/j/621951121?pwd=eWEwVit5WUxlUExOWE51ajdFZnJ2Zz09
Meeting ID: 621 951 121
Passcode: 617076
Title: Almost Disjoint Families under Determinacy, part 1
Abstract: We will investigate some properties of almost disjoint families
and the maximal almost disjoint (MAD) family problem on cardinals (regular
and singular) within determinacy settings. We will show under suitable
assumptions that every almost disjoint family on a cardinal of uncountable
cofinality must be wellorderable. This will show under suitable
assumptions (which includes the boldface GCH) that there are no MAD
families on a regular cardinal kappa so that the family does not strictly
inject into kappa. (This answers a question of Muller concerning
uncountable MAD families on omega_1 under AD.) We will show under AD that
every wellorderable almost disjoint family on a cardinal below Theta of
countable cofinality is not maximal. This result may help explain why the
Schrittesser-Tornquist or Neeman-Norwood arguments excluding a MAD family
on omega has quite a different flavor than the MAD family question for
cardinals of uncountable cofinality. We will review the ultrapower
representation and measure analysis of Jackson below omega_omega. This
will be used to investigate the MAD family question surrounding omega_1,
omega_2, and the singular cardinals omega_n for n between 3 and omega.
This is joint work with Stephen Jackson and Nam Trang.
TUESDAY, November 16, 2021
Set Theory Reading Group: 4:30 P.M., Online, William Chan, Carnegie
Mellon University
Title: Almost Disjoint Families under Determinacy, part 2
Abstract: We will investigate some properties of almost disjoint families
and the maximal almost disjoint (MAD) family problem on cardinals (regular
and singular) within determinacy settings. We will show under suitable
assumptions that every almost disjoint family on a cardinal of uncountable
cofinality must be wellorderable. This will show under suitable
assumptions (which includes the boldface GCH) that there are no MAD
families on a regular cardinal kappa so that the family does not strictly
inject into kappa. (This answers a question of Muller concerning
uncountable MAD families on omega_1 under AD.) We will show under AD that
every wellorderable almost disjoint family on a cardinal below Theta of
countable cofinality is not maximal. This result may help explain why the
Schrittesser-Tornquist or Neeman-Norwood arguments excluding a MAD family
on omega has quite a different flavor than the MAD family question for
cardinals of uncountable cofinality. We will review the ultrapower
representation and measure analysis of Jackson below omega_omega. This
will be used to investigate the MAD family question surrounding omega_1,
omega_2, and the singular cardinals omega_n for n between 3 and omega.
This is joint work with Stephen Jackson and Nam Trang.
Logic Seminar 10 Nov 2021 16:00 hrs by Manat Mustafa, Nazarbayev University, Kazakhstan
NUS Logic Seminar
11/8/2021 22:09:56
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 10 November 2021, 16:00 hrs
Talk via Zoom:
https://nus-sg.zoom.us/j/83049258042?pwd=UWViaWNvTFUrdFdhOHJCdEVydnVkdz09
Meeting ID: 830 4925 8042
Passcode: 1729=x3+y3
Speaker: Manat Mustafa
Title: Rogers semilattices of punctual numberings
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract: The talk employs the punctuality paradigm in the studies of
numberings. We consider the punctual numberings, i.e. uniform computations
for families of primitive recursive functions. The punctual reducibility
between numberings is induced by primitive recursive functions. This
approach gives rise to upper semilattices of degrees, which are called
Rogers pr-semilattices. The main focus of the talk will be the structural
properties of Rogers pr-semilattices. We will show several examples, which
highlight further contrasts between the punctual framework and the
classical theory of computable numberings.
All results are obtained in joint work with Nikolay Bazhenov and
Sergei Ospichev.
This Week in Logic at CUNY
This Week in Logic at CUNY
11/7/2021 17:58:03
This Week in Logic at CUNY:
- - - - Monday, Nov 8, 2021 - - - -
Logic and Metaphysics Workshop
Date: Tomorrow, Monday, November 8th, 4.15-6.15 (NY time)
Speaker: Roman Kossak (CUNY GC)
Title: How undefinable is truth?
Abstract: Almost any set of natural numbers you can think of is first-order definable in the standard model of arithmetic. A notable exception is the set Tr of Gödel numbers of true first-order sentences about addition and multiplication. On the one hand—by Tarski’s undefinability of truth theorem—Tr has no first order definition in the standard model; on the other, it has a straightforward definition in the form of an infinite disjunction of first order formulas. It is definable in a very mild extension of first-order logic. In 1963, Abraham Robinson initiated the study of possible truth assignments for sentences in languages represented in nonstandard models of arithmetic. Such assignments exist, but only in very special models; moreover they are highly non-unique, and—unlike Tr—they are not definable any reasonable formal system. In the talk, I will explain some model theory behind all that and I will talk about some recent results in the study of axiomatic theories of truth.
- - - - Tuesday, Nov 9, 2021 - - - -
Computational Logic Seminar
Tuesday November 9, 2021, 2-4pm,
Eastern Time US
For a zoom link, contact Sergei Artemov (
sartemov@gc.cuny.edu)
Tuesday November 9, 2021.
Speaker: Antonis Achilleos, Reykjavik University
Title: Adventures in Monitorability
Abstract:
I will present recent work on runtime monitorability. Runtime Verification (RV) is the technique of using a monitor to detect the violation or satisfaction of a property at runtime. One question that we ask is what properties we can monitor for. But even before giving an answer, we must first understand what that question means. Although many monitorability definitions exist, few are defined explicitly in terms of the operational guarantees provided by monitors, ie, the computational entities carrying out the verification. We view monitorability as a spectrum, where the fewer guarantees that are required of monitors, the more properties become monitorable. Accordingly, we present a monitorability hierarchy based on this trade-off..
For regular, linear-time specifications, we give syntactic characterisations of the hierarchy in Hennessy-Milner logic with recursion.
We then compare the obtained fragments with previous results for the branching-time setting.
This is joint work with Luca Aceto, Adrian Francalanza, Anna Ingólfsdóttir, and Karoliina Lehtinen.
- - - - Wednesday, Nov 10, 2021 - - - -
- - - - Thursday, Nov 11, 2021 - - - -
- - - - Friday, Nov 12, 2021 - - - -
Set Theory Seminar
CUNY Graduate Center, Room 6417
Friday, November 12, 1pm
The seminar will take place virtually at 1pm US Eastern Standard Time. Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
Tom Benhamou, Tel Aviv University
Intermediate Prikry-type models, quotients, and the Galvin property II
We classify intermediate models of Magidor-Radin generic extensions. It turns out that similar to Gitik Kanovei and Koepke's result, every such intermediate model is of the form V[C] where C is a subsequence of the generic club added by the forcing. The proof uses the Galvin property for normal filters to prove that quotients of some Prikry-type forcings are κ+-c.c. in the generic extension and therefore do not add fresh subsets to κ+. If time permits, we will also present results regarding intermediate models of the Tree-Prikry forcing.
Next Week in Logic at CUNY:
- - - - Monday, Nov 15, 2021 - - - -
Models of Peano Arithmetic (MOPA)
Monday, November 15th, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
Rasmus Blanck, University of Gothenburg
Incompleteness results for arithmetically definable extensions of strong fragments of PA
In this talk, I will present generalisations of some incompleteness results along two axes: r.e. theories are replaced by Σn+1-definable ones, and the base theory is pushed down as far as it will go below PA. Such results are often easy to prove from suitably formulated generalisations of facts used in the original proofs. I will present a handful of such facts, including versions of the arithmetised completeness theorem and the Orey–Hájek characterisation, to show what additional assumptions our theories must satisfy for the results to generalise. Two salient classes of theories emerge in this context: (a) Σn-sound extensions of IΣn + exp, and (b) Πn-complete, consistent extensions of IΣn+1. Finally, I will discuss some results that fail to generalise to Σn+1-definable theories, as well as an open problem related to Woodin's theorem on the universal algorithm.
The presentation is based on the following paper: https://doi.org/10.1017/S1755020321000307
- - - - Tuesday, Nov 16, 2021 - - - -
- - - - Wednesday, Nov 17, 2021 - - - -
The New York City Category Theory Seminar
Department of Computer Science
Department of Mathematics
The Graduate Center of The City University of New York
Time: Wednesdays 07:00 PM Eastern Time (US and Canada)
Speaker: Marco Schorlemmer, Spanish National Research Council.
- - - - Thursday, Nov 18, 2021 - - - -
- - - - Friday, Nov 19, 2021 - - - -
Set Theory Seminar
CUNY Graduate Center, Room 6417
Friday, November 19, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
Corey Switzer, University of Vienna
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
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Barcelona Set theory Seminar
Barcelona Logic Seminar
11/6/2021 12:02:01
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: Yaroslav D. Sergeyev (University of Calabria)
TITLE: Some paradoxes of Infinity revisited
