# Set Theory Talks

Global set theory seminar and conference announcements

## Logic Seminar 17 Aug 2022 17:00 hrs at NUS by Wong Tin Lok

NUS Logic Seminar
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
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
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
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:

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
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!

## Wednesday seminar

Prague Set Theory Seminar
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
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!
View attachment

## Barcelona Set Theory Seminar

Barcelona Logic Seminar

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:

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

## Wednesday seminar

Prague Set Theory Seminar
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
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
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

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:

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

## Cross-Alps Logic Seminar (speaker: Sonia L'Innocente)

Cross-Alps Logic Seminar
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'.

 Mail priva di virus. www.avast.com

## Barcelona Set Theory Seminar

Barcelona Logic Seminar
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:

De: Joan Bagaria <joan.bagaria@icrea.cat>
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:

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

## Barcelona Set Theory Seminar

Barcelona Logic Seminar
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:

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

## Wednesday seminar

Prague Set Theory Seminar
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
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  collection where  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:
I would like to draw attention to the conference
“Functor Categories, Model Theory, and Constructive Category Theory”,
to be held July 11-15, 2022 at the University of Almería, Spain.
https://web.northeastern.edu/martsinkovsky/p/Conferences/Almeria2022/FM.html

- - - - Web Site - - - -

Find us on the web at:  nylogic.github.io
(site designed, built & maintained by Victoria Gitman)

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
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
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:

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

## Wednesday seminar

Prague Set Theory Seminar
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
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'.

 Mail priva di virus. www.avast.com

## (KGRC) (update: Zoom) Logic Colloquium talk Thursday, June 2

Kurt Godel Research Center
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
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)

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
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
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:

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

## (KGRC) Set Theory Research Seminar talks Tuesday, May 24 and WEDNESDAY, May 25

Kurt Godel Research Center

## Cross-Alps Logic Seminar (speaker: Alberto Marcone)

Cross-Alps Logic Seminar
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'.

 Mail priva di virus. www.avast.com

## This Week in Logic at CUNY

This Week in Logic at CUNY
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
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)

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

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:

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

## Wednesday seminar

Prague Set Theory Seminar
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
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
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
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'.

 Mail priva di virus. www.avast.com

## UPDATE: This Week in Logic at CUNY

This Week in Logic at CUNY
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
Julian Schlöder (UConn).

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.

1. Why on earth Gödel [G31] had to introduce this rather strange notion?
2. Does it have any applications in other areas of logic, arithmetical theories, or mathematics?
3. 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!
4. 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 Entropy
Wednesday 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
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)

If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org

## This Week in Logic at CUNY

This Week in Logic at CUNY
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
Julian Schlöder (UConn).

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.

1. Why on earth Gödel [G31] had to introduce this rather strange notion?
2. Does it have any applications in other areas of logic, arithmetical theories, or mathematics?
3. 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!
4. 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 Entropy
Wednesday 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
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)

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
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

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:

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

## (KGRC) Wednesday, May 11: Inaugural Lecture of Matthias Aschenbrenner

Kurt Godel Research Center
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.)
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## Mirna Dzamonja at the Toronto Set Theory Seminar

Set Theory Seminar at the Fields Institute
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
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

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  such that all automorphism orbits of the structure are definable by infinitary  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  if and only if it has a  Scott sentence if and only if it is uniformly  categorical if and only if all its automorphism orbits are  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 , but, other than that, there are no limits to their complexity. Given a completion  of  we give a reduction via bi-interpretability of the class of linear orders to the models of . This allows us to exhibit models of  of Scott rank  for every . In particular, every completion of  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.html
Contact 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
Virtual: Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
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.  that are +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
Julian Schlöder (UConn).

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.

1. Why on earth Gödel [G31] had to introduce this rather strange notion?
2. Does it have any applications in other areas of logic, arithmetical theories, or mathematics?
3. 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!
4. 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 Entropy
Wednesday 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)

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
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
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

El 27 abr 2022, a les 18:10, Joan Bagaria <joan.bagaria@icrea.cat> va escriure:

El 27 gen 2022, a les 21:17, Joan Bagaria <joan.bagaria@icrea.cat> va escriure:

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:

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”.

<BCNSETS2022-2-Boney.pdf>

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

## Barcelona Set Theory Seminar

Barcelona Logic Seminar

El 27 gen 2022, a les 21:17, Joan Bagaria <joan.bagaria@icrea.cat> va escriure:

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:

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

## (KGRC) Set Theory Seminar talk Tuesday, May 3

Kurt Godel Research Center
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.

Conference

## European Set Theory Conference 2022 - second announcement

Cross-Alps Logic Seminar
EUROPEAN SET THEORY CONFERENCE 2022
August 29th-September 2nd, 2022
Turin, Italy

This 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.

We are looking forward to welcoming you in Turin!
Luca Motto Ros (on behalf of the organizers)

-----------------------------------------------

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)
- 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
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
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
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
Virtual (email Victoria Gitman vgitman@nylogic.org for meeting id)

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 -inconsistent. Adding either uniform disquotation or the -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 -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 -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.html
Contact 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
Virtual: Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
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

- - - - 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  such that all automorphism orbits of the structure are definable by infinitary  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  if and only if it has a  Scott sentence if and only if it is uniformly  categorical if and only if all its automorphism orbits are  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 , but, other than that, there are no limits to their complexity. Given a completion  of  we give a reduction via bi-interpretability of the class of linear orders to the models of . This allows us to exhibit models of  of Scott rank  for every . In particular, every completion of  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.html
Contact 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
Virtual: Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
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)

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 (continuation)

IMPAN Working Group in Applications of Set Theory
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
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
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
This Week in Logic at CUNY:

- - - - Monday, Apr 18, 2022 - - - -

- - - - Tuesday, Apr 19, 2022 - - - -

Models of Peano Arithmetic (MOPA)
Monday, April 19, 2pm
Virtual (email Victoria Gitman vgitman@nylogic.org for meeting id)
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
Virtual: Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
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
Virtual (email Victoria Gitman vgitman@nylogic.org for meeting id)

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 -inconsistent. Adding either uniform disquotation or the -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 -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 -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
Virtual: Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
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)

If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org

## CMU seminars this week (logic, model theory, set theory)

Carnegie Mellon Logic Seminar
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
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
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
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
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
Virtual (email Victoria Gitman vgitman@nylogic.org for meeting id)
Thomas Ferguson University of Amsterdam and University of St. Andrews

- - - - Wednesday, Apr 13, 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.html
Contact N Yanofsky for zoom info (noson@sci.brooklyn.cuny.edu)
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
Virtual: Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Joel David Hamkins, Notre Dame University

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  is supercompact if and only if for every second-order sentence true in some structure  (of any size) is also true in a first-order elementary substructure  of size less than . 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
Virtual (email Victoria Gitman vgitman@nylogic.org for meeting id)
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
Virtual: Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
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)

If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org

## Upcoming seminars (logic, model theory, set theory)

Carnegie Mellon Logic Seminar
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
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
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
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'.

 Mail priva di virus. www.avast.com

## This Week in Logic at CUNY

This Week in Logic at CUNY
This Week in Logic at CUNY:

- - - - Monday, Apr 4, 2022 - - - -

Logic and Metaphysics Workshop
Date: Monday, April 4, 4.15-6.15 (NY time), GC 5382
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.

- - - - Tuesday, Apr 5, 2022 - - - -

- - - - Wednesday, Apr 6, 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.html
Contact N Yanofsky for zoom info (noson@sci.brooklyn.cuny.edu)

Speaker:     Jason Parker, Brandon University in Manitoba.

Date and Time:     Wednesday April 6, 2022, 7:00 - 8:30 PM., on Zoom.

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.

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
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
Virtual (email Victoria Gitman vgitman@nylogic.org for meeting id)
Thomas Ferguson University of Amsterdam and University of St. Andrews

- - - - Wednesday, Apr 13, 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.html
Contact N Yanofsky for zoom info (noson@sci.brooklyn.cuny.edu)
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
Virtual: Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
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)

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
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
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
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
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
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
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'.

 Mail priva di virus. www.avast.com

## This Week in Logic at CUNY

This Week in Logic at CUNY
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
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.html
Contact N Yanofsky for zoom info (noson@sci.brooklyn.cuny.edu)

Speaker:     Morgan Rogers, Universita 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 Workshop
Date: Monday, April 4, 4.15-6.15 (NY time), GC 5382
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.

- - - - Tuesday, Apr 5, 2022 - - - -

- - - - Wednesday, Apr 6, 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.html
Contact N Yanofsky for zoom info (noson@sci.brooklyn.cuny.edu)

Speaker:     Jason Parker, Brandon University in Manitoba.

Date and Time:     Wednesday April 6, 2022, 7:00 - 8:30 PM., on Zoom.

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.

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)

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
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
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
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
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
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
Two seminars March 29: Ibarlucía (10:30AM) and Neeman (3:30PM)

## Cross-Alps Logic Seminar (speaker: Omer Ben-Neria)

Cross-Alps Logic Seminar
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'.

 Mail priva di virus. www.avast.com

## Logic Seminar at NUS on Wed 23 March 2022 at 16:00 hrs by Wu Guohua, NTU

NUS Logic Seminar
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
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
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.

- - - - Wednesday, Mar 23, 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.html
Contact N Yanofsky for zoom info (noson@sci.brooklyn.cuny.edu)

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
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.html
Contact N Yanofsky for zoom info (noson@sci.brooklyn.cuny.edu)

Speaker:     Morgan Rogers, Universita 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)"

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
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
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
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
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
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
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
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'.

 Mail priva di virus. www.avast.com

## This Week in Logic at CUNY

This Week in Logic at CUNY
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
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.html
Contact 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
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

- - - - Wednesday, Mar 23, 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.html
Contact N Yanofsky for zoom info (noson@sci.brooklyn.cuny.edu)

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)"

If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org

## Jakub Andruszkiewicz, The club principle and its connections to the diamond principle

IMPAN Working Group in Applications of Set Theory
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
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
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
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
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
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'.

 Mail priva di virus. www.avast.com

## This Week in Logic at CUNY

This Week in Logic at CUNY
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
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  of infinite words over a countable alphabet  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  guesses for alphabets of finite size . Meanwhile, for some dictionaries on an infinite alphabet, infinite play is required, but the code-breaker can always win by stage  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 , 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 , 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  of the meager ideal and bounded above by the covering number . In particular, the precise value of the mastermind number is independent of ZFC and can consistently be strictly between  and the continuum . 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 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
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.html
Contact 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)"

If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org

## CMU math logic seminar on Tuesday, March 15

Carnegie Mellon Logic Seminar
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
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

## Cross-Alps Logic Seminar (speaker: Michal Skrzypczak)

Cross-Alps Logic Seminar
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:

Number Meeting: 2733 686 2768

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.

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## This Week in Logic at CUNY

This Week in Logic at CUNY
This Week in Logic at CUNY:

- - - - Monday, Feb 28, 2022 - - - -

Logic and Metaphysics Workshop
Date: Monday, February 28, 4.15-6.15 (NY time), GC 5382
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 strategically closed forcings of cardinality strategically closed forcings of cardinality  and the distributive forcing notions of cardinality . Then we will examine distributive subforcings of the Prikry forcing of cardinality larger than . 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
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.html
Contact 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  of infinite words over a countable alphabet  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  guesses for alphabets of finite size . Meanwhile, for some dictionaries on an infinite alphabet, infinite play is required, but the code-breaker can always win by stage  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 , 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 , 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  of the meager ideal and bounded above by the covering number . In particular, the precise value of the mastermind number is independent of ZFC and can consistently be strictly between  and the continuum . 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 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)"

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
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

Conference

## Logic Seminar Wed 2 March 2022 16:00 hrs at NUS by Lavinia Picollo

NUS Logic Seminar
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

## Mariam Beriashvili @ Toronto Set Theory Seminar // UNUSUAL TIME

Set Theory Seminar at the Fields Institute
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
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
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:

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

## Piotr Koszmider, Bidiscrete system in compact spaces

IMPAN Working Group in Applications of Set Theory
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

## Wednesday seminar

Prague Set Theory Seminar
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
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
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:

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

## Kamil Ryduchowski; A Banach space admitting few operators

IMPAN Working Group in Applications of Set Theory
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
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
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
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
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 -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) -sound extensions of I + exp, and (b) -complete, consistent extensions of I. Finally, I will discuss some results that fail to generalise to -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
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  (or even just 'every real is constructible') then there is a  well order of the reals and  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  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 , there is a  well order of the reals, and a  MAD family, a  ultrafilter base for a P-point, and a  maximal independent family, all of size . 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  . 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)
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)

If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org

## Kamil Ryduchowski; An antiramsey coloring of pairs

IMPAN Working Group in Applications of Set Theory
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

## Two talks next Tuesday

Carnegie Mellon Logic Seminar

## Logic Seminar 10 Nov 2021 16:00 hrs by Manat Mustafa, Nazarbayev University, Kazakhstan

NUS Logic Seminar
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
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 SeminarTuesday November 9, 2021, 2-4pm,  Eastern Time USFor a zoom link, contact Sergei Artemov (sartemov@gc.cuny.edu)Tuesday November 9, 2021.

Speaker: Antonis Achilleos, Reykjavik University

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
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  where  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 -c.c. in the generic extension and therefore do not add fresh subsets to . 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 -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) -sound extensions of I + exp, and (b) -complete, consistent extensions of I. Finally, I will discuss some results that fail to generalise to -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
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)