## Logic Seminar Wednesday 10 Aug 2022 17:00 hrs at NUS, Room S17#04-05

## Wednesday seminar

## Barcelona Set Theory Seminar

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

## Wednesday seminar

## (KGRC) seminar talks Tuesday, June 28 and Thursday, June 30

## Barcelona Set Theory Seminar

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

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

## Wednesday seminar

## Wednesday seminar

## Krzysztof Zakrzewski, Elementary submodels and Corson-compact spaces

## Barcelona Set Theory Seminar

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)

**Sonia L'Innocente**(University of Camerino)

will give a talk on

*A factorisation theory for generalised power series*Please refer to the usual webpage of our LogicGroup for more details and the abstract of the talk.

The seminar will be held remotely through Webex. Please write to luca.mottoros [at] unito [dot] itfor the link to the event.

The Cross-Alps Logic Seminar is co-organized by the logic groups of Genoa, Lausanne, Turin and Udine as part of our collaboration in the project PRIN 2017 'Mathematical logic: models, sets, computability'.

## Barcelona Set Theory Seminar

Inici del missatge reenviat:De:Joan Bagaria <joan.bagaria@icrea.cat>Tema:Barcelona Set Theory SeminarData:3 de juny de 2022, 8:56:35 CESTDear All,Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.SPEAKER: William ManceTITLE: Descriptive complexity in number theory and dynamicsDATE: 8 June 2022TIME: 16:00 (CEST)PLACE: The Seminar will take place online via Zoom:Meeting ID: 985 6524 7347Passcode: 243408Best regards,JoanP.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

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

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

## This Week in Logic at CUNY

- - - - Tuesday, May 31, 2022 - - - -

Models of Peano Arithmetic (MOPA)

Tuesday, May 31, 8pm

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

**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 - - - -

- - - - Monday, Jun 6, 2022 - - - -

- - - - Tuesday, Jun 7, 2022 - - - -

- - - - Wednesday, Jun 8, 2022 - - - -

- - - - Thursday, Jun 9, 2022 - - - -

- - - - Friday, Jun 10, 2022 - - - -

- - - - Other Logic News - - - -

“Functor Categories, Model Theory, and Constructive Category Theory”,

to be held July 11-15, 2022 at the University of Almería, Spain.

For more information visit

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)

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

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

## Jakub Andruszkiewicz, Countable support iterations of proper forcing notions

## Barcelona Set Theory Seminar

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

## Cross-Alps Logic Seminar (speaker: Takako Nemoto)

**Takako Nemoto**(Japan Advanced Institute of Science and Technology)

will give a talk on

*Determinacy of infinite games and reverse mathematics*Please refer to the usual webpage of our LogicGroup for more details and the abstract of the talk.

The seminar will be held remotely through Webex. Please write to luca.mottoros [at] unito [dot] itfor the link to the event.

The Cross-Alps Logic Seminar is co-organized by the logic groups of Genoa, Lausanne, Turin and Udine as part of our collaboration in the project PRIN 2017 'Mathematical logic: models, sets, computability'.

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

## 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)

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 - - - -

CUNY Graduate Center, Friday, May 27, 12:15pm

In-person: GC Room 6496

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

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.

- - - - 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)

- - - - Wednesday, Jun 1, 2022 - - - -

- - - - Thursday, Jun 2, 2022 - - - -

- - - - Friday, Jun 3, 2022 - - - -

- - - - Other Logic News - - - -

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io

(site designed, built & maintained by Victoria Gitman)

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

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

## Wednesday seminar

## Barcelona Set Theory Seminar

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

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

**Alberto Marcone**(University of Udine)

will give a talk on

*The transfinite Ramsey theorem*Please refer to the usual webpage of our LogicGroup for more details and the abstract of the talk.

The seminar will be held remotely through Webex. Please write to luca.mottoros [at] unito [dot] it for the link to the event.

The Cross-Alps Logic Seminar is co-organized by the logic groups of Genoa, Lausanne, Turin and Udine as part of our collaboration in the project PRIN 2017 'Mathematical logic: models, sets, computability'.

## This Week in Logic at CUNY

- - - - Monday, May 16, 2022 - - - -

Logic and Metaphysics Workshop

Date: Monday, May 16, 4.15-6.15 (NY time), GC 5382

For meeting information (including zoom link for those wishing to attend remotely), please sign up for our mailing list at https://logic.commons.gc.cuny.edu/about/

Mircea Dumitru (Bucharest)

Title: Modal Frame Incompleteness: An Account through Second Order Logic

Abstract: Propositional modal logic is usually viewed as a generalization and extension of propositional classical logic. The main argument of this paper is that a good case can be made that modal logic should be construed as a restricted form of second order classical logic. The paper makes use of the embedding of modal logic in second order logic and henceforth it goes on examining one aspect of this second order connection having to do with an incompleteness phenomenon. The leading concept is that modal incompleteness is to be explained as a kind of exemplification of standard order incompleteness. Moreover the modal incompleteness phenomenon is essentially rooted in the weaker expressive power of the language of sentential modal logic as compared to the stronger expressive power of the language of second order logic.

- - - - Tuesday, May 17, 2022 - - - -

Models of Peano Arithmetic (MOPA)

Tuesday, May 17, 2pm

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

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 - - - -

CUNY Graduate Center, Friday, May 20, 12:15pm

In-person: GC Room 6496

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

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.

- - - - Monday, May 23, 2022 - - - -

- - - - Tuesday, May 24, 2022 - - - -

- - - - Wednesday, May 25, 2022 - - - -

- - - - Thursday, May 26, 2022 - - - -

- - - - Friday, May 27, 2022 - - - -

CUNY Graduate Center, Friday, May 27, 12:15pm

In-person: GC Room 6496

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

Determinacy and Partition Properties: Part II

In this talk, we will review some basic properties of partition cardinals under the axiom of determinacy. We will be particularly interested with the strong partition property of the first uncountable cardinal and the good coding system used to derive these partition properties. We will discuss almost everywhere behavior of functions on partition spaces of cardinals with respect to the partition measures including various almost everywhere continuity and monotonicity properties. These continuity results will be used to distinguish some cardinalities below the power set of partition cardinals. We will also use these continuity results to produce upper bounds on the ultrapower of the first uncountable cardinal by each of its partition measures, which addresses a question of Goldberg. Portions of the talk are joint work with Jackson and Trang.

- - - - Other Logic News - - - -

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io

(site designed, built & maintained by Victoria Gitman)

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

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

## Barcelona Set Theory Seminar

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

## (KGRC) Set Theory Research Seminar talk Tuesday, May 17 and Logic Colloquium talk Thursday, May 19

## TOMORROW: Vladimir Tkachuk at the Toronto Set Theory Seminar

## Cross-Alps Logic Seminar (speaker: Udayan B. Darji)

**Udayan B. Darji**(University of Louisville)

will give a talk on

*Descriptive complexity and local entropy*Please refer to the usual webpage of our LogicGroup for more details and the abstract of the talk.

The seminar will be held remotely through Webex. Please write to luca.mottoros [at] unito [dot] itfor the link to the event.

The Cross-Alps Logic Seminar is co-organized by the logic groups of Genoa, Lausanne, Turin and Udine as part of our collaboration in the project PRIN 2017 'Mathematical logic: models, sets, computability'.

## UPDATE: This Week in Logic at CUNY

Logic and Metaphysics Workshop

Date: Monday, May 9, 4.15-6.15 (NY time), GC 5382

For meeting information (including zoom link for those wishing to attend remotely), please sign up for our mailing list at https://logic.commons.gc.cuny.edu/about/

Julian Schlöder (UConn).

Title: Neo-Pragmatism about Truth

Abstract: Deflationists about truth hold that the function of the truth predicate is to enable us to make certain assertions we could not otherwise make. Pragmatists claim that the utility of negation lies in its role in registering incompatibility. The pragmatist insight about negation has been successfully incorporated into bilateral theories of content, which take the meaning of negation to be inferentially explained in terms of the speech act of rejection. One can implement the deflationist insight in the pragmatist’s theory of content by taking the meaning of the truth predicate to be explained by its inferential relation to assertion. There are two upshots. First, a new diagnosis of the Liar, Revenges and attendant paradoxes: the paradoxes require that truth rules preserve evidence, but they only preserve commitment. Second, one straightforwardly obtains axiomatisations of several supervaluational hierarchies, answering the question of how such theories are to be naturally axiomatised. This is joint work with Luca Incurvati (Amsterdam).

- - - - Tuesday, May 10, 2022 - - - -

Models of Peano Arithmetic (MOPA)

Tuesday, May 10, 10am

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

**Saeed Salehi**, University of Tabriz*ω*-Consistency: Gödel’s “much weaker” notion of soundness

As the history goes, and was confirmed recently [vP20], Gödel first proved his first incompleteness theorem [G31] for *sound* theories (that extend *Principia Mathematica*). Later he weakened the soundness condition to “ℵ0-consistency”, which later evolved to “*ω*-consistency”. This condition was needed for irrefutability of (what is now called) Gödelian sentences; the simple consistency of a theory suffices for the unprovability of such sentences. Gödel already notes in [G31] that a necessary and sufficient condition for the independence of Gödelian sentences of *T* is just a bit more than the simple consistency of *T*: the consistency of *T* with Con*T*, the consistency statement of *T*.

In this talk, we ask the following questions and attempt at answering them, at least partially.

- Why on earth Gödel [G31] had to introduce this rather strange notion?
- Does it have any applications in other areas of logic, arithmetical theories, or mathematics?
- What was Gödel’s reason that
*ω*-consistency is “much weaker” than soundness? He does prove in [G31] that consistency is weaker (if not much weaker) than*ω*-consistency; but never mentions a proof or even a hint as to why soundness is (much) stronger than*ω*-consistency! - Other than those historical and philosophical questions, is this a useful notion worthy of further study?

*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.),, Oxford University Press, 1986, pp. 135–152.*Kurt Gödel: Collected Works, Vol. I: Publications 1929–1936* - [vP20] Jan von Plato (2020);
, Springer.*Can Mathematics Be Proved Consistent? Gödel’s Shorthand Notes & Lectures on Incompleteness*

Reviewed in the**zbMATH**Open at`https://zbmath.org/1466.03001`

- - - - Wednesday, May 11, 2022 - - - -

Tutorial: Categorical Semantics of Entropy

CUNY Graduate Center, Friday, May 13, 12:15pm

In-person: GC Room 6496

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

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

- - - - Monday, May 16, 2022 - - - -

Logic and Metaphysics Workshop

Date: Monday, May 16, 4.15-6.15 (NY time), GC 5382

For meeting information (including zoom link for those wishing to attend remotely), please sign up for our mailing list at https://logic.commons.gc.cuny.edu/about/

Mircea Dumitru (Bucharest)

Title: Modal Frame Incompleteness: An Account through Second Order Logic

Abstract: Propositional modal logic is usually viewed as a generalization and extension of propositional classical logic. The main argument of this paper is that a good case can be made that modal logic should be construed as a restricted form of second order classical logic. The paper makes use of the embedding of modal logic in second order logic and henceforth it goes on examining one aspect of this second order connection having to do with an incompleteness phenomenon. The leading concept is that modal incompleteness is to be explained as a kind of exemplification of standard order incompleteness. Moreover the modal incompleteness phenomenon is essentially rooted in the weaker expressive power of the language of sentential modal logic as compared to the stronger expressive power of the language of second order logic.

- - - - Tuesday, May 17, 2022 - - - -

Models of Peano Arithmetic (MOPA)

Tuesday, May 17, 2pm

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

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 - - - -

CUNY Graduate Center, Friday, May 20, 12:15pm

In-person: GC Room 6496

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

Determinacy and Partition Properties

In this talk, we will review some basic properties of partition cardinals under the axiom of determinacy. We will be particularly interested with the strong partition property of the first uncountable cardinal and the good coding system used to derive these partition properties. We will discuss almost everywhere behavior of functions on partition spaces of cardinals with respect to the partition measures including various almost everywhere continuity and monotonicity properties. These continuity results will be used to distinguish some cardinalities below the power set of partition cardinals. We will also use these continuity results to produce upper bounds on the ultrapower of the first uncountable cardinal by each of its partition measures, which addresses a question of Goldberg. Portions of the talk are joint work with Jackson and Trang.

- - - - Other Logic News - - - -

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io

(site designed, built & maintained by Victoria Gitman)

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

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

## This Week in Logic at CUNY

Logic and Metaphysics Workshop

Date: Monday, May 9, 4.15-6.15 (NY time), GC 5382

For meeting information (including zoom link for those wishing to attend remotely), please sign up for our mailing list at https://logic.commons.gc.cuny.edu/about/

Julian Schlöder (UConn).

Title: Neo-Pragmatism about Truth

Abstract: Deflationists about truth hold that the function of the truth predicate is to enable us to make certain assertions we could not otherwise make. Pragmatists claim that the utility of negation lies in its role in registering incompatibility. The pragmatist insight about negation has been successfully incorporated into bilateral theories of content, which take the meaning of negation to be inferentially explained in terms of the speech act of rejection. One can implement the deflationist insight in the pragmatist’s theory of content by taking the meaning of the truth predicate to be explained by its inferential relation to assertion. There are two upshots. First, a new diagnosis of the Liar, Revenges and attendant paradoxes: the paradoxes require that truth rules preserve evidence, but they only preserve commitment. Second, one straightforwardly obtains axiomatisations of several supervaluational hierarchies, answering the question of how such theories are to be naturally axiomatised. This is joint work with Luca Incurvati (Amsterdam).

- - - - Tuesday, May 10, 2022 - - - -

Models of Peano Arithmetic (MOPA)

Tuesday, May 10, 2pm

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

**Saeed Salehi**, University of Tabriz*ω*-Consistency: Gödel’s “much weaker” notion of soundness

As the history goes, and was confirmed recently [vP20], Gödel first proved his first incompleteness theorem [G31] for *sound* theories (that extend *Principia Mathematica*). Later he weakened the soundness condition to “ℵ0-consistency”, which later evolved to “*ω*-consistency”. This condition was needed for irrefutability of (what is now called) Gödelian sentences; the simple consistency of a theory suffices for the unprovability of such sentences. Gödel already notes in [G31] that a necessary and sufficient condition for the independence of Gödelian sentences of *T* is just a bit more than the simple consistency of *T*: the consistency of *T* with Con*T*, the consistency statement of *T*.

In this talk, we ask the following questions and attempt at answering them, at least partially.

- Why on earth Gödel [G31] had to introduce this rather strange notion?
- Does it have any applications in other areas of logic, arithmetical theories, or mathematics?
- What was Gödel’s reason that
*ω*-consistency is “much weaker” than soundness? He does prove in [G31] that consistency is weaker (if not much weaker) than*ω*-consistency; but never mentions a proof or even a hint as to why soundness is (much) stronger than*ω*-consistency! - Other than those historical and philosophical questions, is this a useful notion worthy of further study?

*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.),, Oxford University Press, 1986, pp. 135–152.*Kurt Gödel: Collected Works, Vol. I: Publications 1929–1936* - [vP20] Jan von Plato (2020);
, Springer.*Can Mathematics Be Proved Consistent? Gödel’s Shorthand Notes & Lectures on Incompleteness*

Reviewed in the**zbMATH**Open at`https://zbmath.org/1466.03001`

- - - - Wednesday, May 11, 2022 - - - -

Tutorial: Categorical Semantics of Entropy

CUNY Graduate Center, Friday, May 13, 12:15pm

In-person: GC Room 6496

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

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

- - - - Monday, May 16, 2022 - - - -

Logic and Metaphysics Workshop

Date: Monday, May 16, 4.15-6.15 (NY time), GC 5382

For meeting information (including zoom link for those wishing to attend remotely), please sign up for our mailing list at https://logic.commons.gc.cuny.edu/about/

Mircea Dumitru (Bucharest)

Title: Modal Frame Incompleteness: An Account through Second Order Logic

Abstract: Propositional modal logic is usually viewed as a generalization and extension of propositional classical logic. The main argument of this paper is that a good case can be made that modal logic should be construed as a restricted form of second order classical logic. The paper makes use of the embedding of modal logic in second order logic and henceforth it goes on examining one aspect of this second order connection having to do with an incompleteness phenomenon. The leading concept is that modal incompleteness is to be explained as a kind of exemplification of standard order incompleteness. Moreover the modal incompleteness phenomenon is essentially rooted in the weaker expressive power of the language of sentential modal logic as compared to the stronger expressive power of the language of second order logic.

- - - - Tuesday, May 17, 2022 - - - -

Models of Peano Arithmetic (MOPA)

Tuesday, May 17, 2pm

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

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 - - - -

CUNY Graduate Center, Friday, May 20, 12:15pm

In-person: GC Room 6496

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

Determinacy and Partition Properties

In this talk, we will review some basic properties of partition cardinals under the axiom of determinacy. We will be particularly interested with the strong partition property of the first uncountable cardinal and the good coding system used to derive these partition properties. We will discuss almost everywhere behavior of functions on partition spaces of cardinals with respect to the partition measures including various almost everywhere continuity and monotonicity properties. These continuity results will be used to distinguish some cardinalities below the power set of partition cardinals. We will also use these continuity results to produce upper bounds on the ultrapower of the first uncountable cardinal by each of its partition measures, which addresses a question of Goldberg. Portions of the talk are joint work with Jackson and Trang.

- - - - Other Logic News - - - -

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io

(site designed, built & maintained by Victoria Gitman)

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

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

## Wednesday seminar

## Barcelona Set Theory Seminar

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

## Mirna Dzamonja at the Toronto Set Theory Seminar

## This Week in Logic at CUNY

Logic and Metaphysics Workshop

Date: Monday, May 2, 4.15-6.15 (NY time), GC 5382

For meeting information (including zoom link for those wishing to attend remotely), please sign up for our mailing list at https://logic.commons.gc.cuny.edu/about/

Elia Zardini (Madrid)

- - - - Tuesday, May 3, 2022 - - - -

Models of Peano Arithmetic (MOPA)

Tuesday, May 3, 2pm

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

**Dino Rossegger**, UC Berkeley and TU Wien**The structural complexity of models of PA**

The Scott rank of a countable structure is the least ordinal 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 - - - -

CUNY Graduate Center, Friday, May 6, 12:15pm

**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.

Friday, May 6, 2:00-3:30pm

- - - - Monday, May 9, 2022 - - - -

Logic and Metaphysics Workshop

Date: Monday, May 9, 4.15-6.15 (NY time), GC 5382

For meeting information (including zoom link for those wishing to attend remotely), please sign up for our mailing list at https://logic.commons.gc.cuny.edu/about/

Julian Schlöder (UConn).

Title: Neo-Pragmatism about Truth

Abstract: Deflationists about truth hold that the function of the truth predicate is to enable us to make certain assertions we could not otherwise make. Pragmatists claim that the utility of negation lies in its role in registering incompatibility. The pragmatist insight about negation has been successfully incorporated into bilateral theories of content, which take the meaning of negation to be inferentially explained in terms of the speech act of rejection. One can implement the deflationist insight in the pragmatist’s theory of content by taking the meaning of the truth predicate to be explained by its inferential relation to assertion. There are two upshots. First, a new diagnosis of the Liar, Revenges and attendant paradoxes: the paradoxes require that truth rules preserve evidence, but they only preserve commitment. Second, one straightforwardly obtains axiomatisations of several supervaluational hierarchies, answering the question of how such theories are to be naturally axiomatised. This is joint work with Luca Incurvati (Amsterdam).

- - - - Tuesday, May 10, 2022 - - - -

Models of Peano Arithmetic (MOPA)

Tuesday, May 10, 2pm

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

**Saeed Salehi**, University of Tabriz*ω*-Consistency: Gödel’s “much weaker” notion of soundness

As the history goes, and was confirmed recently [vP20], Gödel first proved his first incompleteness theorem [G31] for *sound* theories (that extend *Principia Mathematica*). Later he weakened the soundness condition to “ℵ0-consistency”, which later evolved to “*ω*-consistency”. This condition was needed for irrefutability of (what is now called) Gödelian sentences; the simple consistency of a theory suffices for the unprovability of such sentences. Gödel already notes in [G31] that a necessary and sufficient condition for the independence of Gödelian sentences of *T* is just a bit more than the simple consistency of *T*: the consistency of *T* with Con*T*, the consistency statement of *T*.

In this talk, we ask the following questions and attempt at answering them, at least partially.

- Why on earth Gödel [G31] had to introduce this rather strange notion?
- Does it have any applications in other areas of logic, arithmetical theories, or mathematics?
- What was Gödel’s reason that
*ω*-consistency is “much weaker” than soundness? He does prove in [G31] that consistency is weaker (if not much weaker) than*ω*-consistency; but never mentions a proof or even a hint as to why soundness is (much) stronger than*ω*-consistency! - Other than those historical and philosophical questions, is this a useful notion worthy of further study?

*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.),, Oxford University Press, 1986, pp. 135–152.*Kurt Gödel: Collected Works, Vol. I: Publications 1929–1936* - [vP20] Jan von Plato (2020);
, Springer.*Can Mathematics Be Proved Consistent? Gödel’s Shorthand Notes & Lectures on Incompleteness*

Reviewed in the**zbMATH**Open at`https://zbmath.org/1466.03001`

- - - - Wednesday, May 11, 2022 - - - -

Tutorial: Categorical Semantics of Entropy

CUNY Graduate Center, Friday, May 13, 12:15pm

In-person: GC Room 6496

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

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

- - - - Other Logic News - - - -

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io

(site designed, built & maintained by Victoria Gitman)

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

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

## Wednesday seminar

## Barcelona Set Theory Seminar

El 27 abr 2022, a les 18:10, Joan Bagaria <joan.bagaria@icrea.cat> va escriure:<BCNSETS2022-2-Boney.pdf>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 BoneyTITLE: Compactness of strong logics and large cardinalsDATE: 4 May 2022TIME: 16:00 (CET)PLACE: The Seminar will take place online via Zoom:Meeting ID: 985 6524 7347Passcode: 243408Best regards,JoanP.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

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

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

## XIX Latin American Symposium of Mathematical Logic (SLALM), Costa Rica, July 26-30

## European Set Theory Conference 2022 - second announcement

**EUROPEAN SET THEORY CONFERENCE 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.

IMPORTANT DEADLINES:

30/04/2022: Abstract submission for contributed talks

30/06/2022: Early registration with reduced fee

22/08/2022: Registration

MORE ON THE CONFERENCE:

The European Set Theory Conferences is a series of biannual meetings coordinated by the European Set Theory Society (ESTS). This year's edition is organized by the Department of Mathematics of the University of Turin and ESTS, in partnership with the Clay Mathematics Institute. It is the most important conference in set theory, and gathers the worldwide leaders in the field as well as many young researchers. During the event, the prestigious Hausdorff medal will be awarded for the most influential work in set theory published in the preceding five years. There will also be a special session in honor of Boban Veličković's 60th birthday.

**Invited speakers**

- Jeffrey Bergfalk (University of Vienna)

- Filippo Calderoni (University of Illinois Chicago)

- Natasha Dobrinen (University of Denver)

- Osvaldo Guzmán (Universidad Nacional Autónoma de México)

- Joel Hamkins (University of Notre Dame)

- Chris Lambie-Hanson (Czech Academy of Sciences)

- Martino Lupini (Victoria University of Wellington)

- Julien Melleray (Université de Lyon)

- Andrew Marks (University of California, Los Angeles)

- Sandra Müller (TU Wien)

- Saharon Shelah (Hebrew University of Jerusalem)

- Stevo Todorčević (University of Toronto and Centre national de la recherche scientifique)

- Jouko Väänänen (University of Helsinki)

- Zoltán Vidnyánsky (California Institute of Technology)

- Trevor Wilson (Miami University, Oxford Ohio)

**Tutorials**

- Yair Hayut (Hebrew University of Jerusalem)

- Grigor Sargsyan (Polish Academy of Sciences)

**Boban**

**Veličković's 60th Birthday Celebration**

- Laura Fontanella (Université Paris-Est Créteil)

- Rahman Mohammadpour (TU Wien)

- Giorgio Venturi (University of Campinas)

- Matteo Viale (University of Turin)

**Scientific committee**

Joan Bagaria (chair), Matthew Foreman, Moti Gitik, Péter Komjáth, Piotr Koszmider, Heike Mildenberger, Luca Motto Ros, John Steel

**Local organizing committee**

Alessandro Andretta, Raphaël Carroy, Luca Motto Ros, Gianluca Paolini, Francesco Parente, Salvatore Scamperti, Matteo Viale

## Matteo Viale at the Toronto Set Theory Seminar

## This Week in Logic at CUNY

Date: Monday, April 25, 4.15-6.15 (NY time), GC 5382

For meeting information (including zoom link for those wishing to attend remotely), please sign up for our mailing list at https://logic.commons.gc.cuny.edu/about/

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 - - - -

Tuesday, April 26, 2pm

Michał Godziszewski, University of Vienna**Modal Quantifiers, Potential Infinity, and Yablo sequences**

When properly arithmetized, Yablo's paradox results in a set of formulas which (with local disquotation in the background) turns out to be consistent, but -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 - - - -

CUNY Graduate Center, Friday, April 29, 12:15pm

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.

- - - - Monday, May 2, 2022 - - - -

Logic and Metaphysics Workshop

Date: Monday, May 2, 4.15-6.15 (NY time), GC 5382

For meeting information (including zoom link for those wishing to attend remotely), please sign up for our mailing list at https://logic.commons.gc.cuny.edu/about/

Elia Zardini (Madrid)

- - - - Tuesday, May 3, 2022 - - - -

Models of Peano Arithmetic (MOPA)

Tuesday, May 3, 2pm

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

**Dino Rossegger**, UC Berkeley and TU Wien**The structural complexity of models of PA**

The Scott rank of a countable structure is the least ordinal 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 - - - -

CUNY Graduate Center, Friday, May 6, 12:15pm

- - - - Other Logic News - - - -

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io

(site designed, built & maintained by Victoria Gitman)

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

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

## Kacper Kucharski, Using elementary submodels in topology (continuation)

## Wednesday seminar

## TOMORROW: Asger Törnquist at 13:30 EDT

## This Week in Logic at CUNY

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

Monday, April 19, 2pm

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 - - - -

CUNY Graduate Center, Friday, April 22, 12:15pm

**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.

- - - - Monday, Apr 25, 2022 - - - -

- - - - Tuesday, Apr 26, 2022 - - - -

Monday, April 26, 2pm

Michał Godziszewski, University of Vienna**Modal Quantifiers, Potential Infinity, and Yablo sequences**

When properly arithmetized, Yablo's paradox results in a set of formulas which (with local disquotation in the background) turns out to be consistent, but -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 - - - -

CUNY Graduate Center, Friday, April 29, 12:15pm

- - - - Other Logic News - - - -

CONFERENCE ANNOUNCEMENT:

Venue: online (information will be provided to registered participants)

Logicians participating in this conference stand united for Peace. The on-going Russian military invasion in Ukraine is causing death, destruction and it is the direct cause of a gigantic humanitarian crisis. Educational facilities have been hit, supply chains have been broken and people have lost their families and homes. By organizing this conference, we offer our moral and financial support to our colleagues in Ukraine in this time of war.

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io

(site designed, built & maintained by Victoria Gitman)

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

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

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

## Wednesday seminar

## Wednesday seminar

## This Week in Logic at CUNY

Logic and Metaphysics Workshop

Date: Monday, April 11, 4.15-6.15 (NY time), GC 5382

For meeting information (including zoom link for those wishing to attend remotely), please sign up for our mailing list at https://logic.commons.gc.cuny.edu/about/

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

- - - - 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)

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 - - - -

CUNY Graduate Center, Friday, April 15, 12:15pm

**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

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

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

Monday, April 19, 2pm

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 - - - -

CUNY Graduate Center, Friday, April 22, 12:15pm

- - - - Other Logic News - - - -

CONFERENCE ANNOUNCEMENT:

Venue: online (information will be provided to registered participants)

Logicians participating in this conference stand united for Peace. The on-going Russian military invasion in Ukraine is causing death, destruction and it is the direct cause of a gigantic humanitarian crisis. Educational facilities have been hit, supply chains have been broken and people have lost their families and homes. By organizing this conference, we offer our moral and financial support to our colleagues in Ukraine in this time of war.

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io

(site designed, built & maintained by Victoria Gitman)

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

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

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

## Logic Seminar 13 April 2022 16:00 hrs at NUS by Wang Wei, Sun Yatsen University

## Logic Seminar 6 April 2022 16:00 hrs by Frank Stephan, NUS

## Cross-Alps Logic Seminar (speaker: Alexander S. Kechris)

**Alexander S. Kechris**(Caltech)

will give a talk on

*Countable sections for actions of locally compact groups*Please refer to the usual webpage of our LogicGroup for more details and the abstract of the talk.

The seminar will be held remotely through Webex. Please write to luca.mottoros [at] unito [dot] itfor the link to the event.

The Cross-Alps Logic Seminar is co-organized by the logic groups of Genoa, Lausanne, Turin and Udine as part of our collaboration in the project PRIN 2017 'Mathematical logic: models, sets, computability'.

## This Week in Logic at CUNY

Logic and Metaphysics Workshop

Date: Monday, April 4, 4.15-6.15 (NY time), GC 5382

For meeting information (including zoom link for those wishing to attend remotely), please sign up for our mailing list at https://logic.commons.gc.cuny.edu/about/

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.**

Title:** Enriched structure-semantics adjunctions and monad-theory equivalences for subcategories of arities.**

Abstract: Several structure-semantics adjunctions and monad-theory equivalences have been established in category theory. Lawvere (1963) developed a structure-semantics adjunction between Lawvere theories and tractable Set-valued functors, which was subsequently generalized by Linton (1969), while Dubuc (1970) established a structure-semantics adjunction between V-theories and tractable V-valued V-functors for a symmetric monoidal closed category V. It is also well known (and due to Linton) that there is an equivalence between Lawvere theories and finitary monads on Set. Generalizing this result, Lucyshyn-Wright (2016) established a monad-theory equivalence for eleutheric systems of arities in arbitrary closed categories. Building on earlier work by Nishizawa and Power, Bourke and Garner (2019) subsequently proved a general monad-theory equivalence for arbitrary small subcategories of arities in locally presentable enriched categories. However, neither of these equivalences generalizes the other, and there has not yet been a general treatment of enriched structure-semantics adjunctions that specializes to those established by Lawvere, Linton, and Dubuc.

Motivated by these considerations, we develop a general axiomatic framework for studying enriched structure-semantics adjunctions and monad-theory equivalences for subcategories of arities, which generalizes all of the aforementioned results and also provides substantial new examples of relevance for topology and differential geometry. For a subcategory of arities J in a V-category C over a symmetric monoidal closed category V, Linton’s notion of clone generalizes to provide enriched notions of J-theory and J-pretheory, which were also employed by Bourke and Garner (2019). We say that J is amenable if every J-theory admits free algebras, and is strongly amenable if every J-pretheory admits free algebras. If J is amenable, then we obtain an idempotent structure-semantics adjunction between certain J-pretheories and J-tractable V-categories over C, which yields an equivalence between J-theories and J-nervous V-monads on C. If J is strongly amenable, then we also obtain a rich theory of presentations for J-theories and J-nervous V-monads. We show that many previously studied subcategories of arities are (strongly) amenable, from which we recover the aforementioned structure-semantics adjunctions and monad-theory equivalences. We conclude with the result that any small subcategory of arities in a locally bounded closed category is strongly amenable, from which we obtain structure-semantics adjunctions and monad-theory equivalences in (e.g.) many convenient categories of spaces.

Joint work with Rory Lucyshyn-Wright.

- - - - Thursday, Apr 7, 2022 - - - -

- - - - Friday, Apr 8, 2022 - - - -

- - - - Monday, Apr 11, 2022 - - - -

Logic and Metaphysics Workshop

Date: Monday, April 11, 4.15-6.15 (NY time), GC 5382

For meeting information (including zoom link for those wishing to attend remotely), please sign up for our mailing list at https://logic.commons.gc.cuny.edu/about/

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

- - - - 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)

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 - - - -

CUNY Graduate Center, Friday, April 1, 12:15pm

- - - - Other Logic News - - - -

CONFERENCE ANNOUNCEMENT:

Venue: online (information will be provided to registered participants)

Logicians participating in this conference stand united for Peace. The on-going Russian military invasion in Ukraine is causing death, destruction and it is the direct cause of a gigantic humanitarian crisis. Educational facilities have been hit, supply chains have been broken and people have lost their families and homes. By organizing this conference, we offer our moral and financial support to our colleagues in Ukraine in this time of war.

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io

(site designed, built & maintained by Victoria Gitman)

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

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

## Damian Sobota, Measures with the Additive Property and the random forcing

## Next math logic seminar on Tuesday

## Wednesday seminar

## (KGRC) Set Theory Research Seminar talk on Tuesday, April 5

## Toronto Set Theory Seminar

## Cross-Alps Logic Seminar (speaker: David Evans)

**David Evans**(Imperial College London)

will give a talk on

*Amalgamation properties in measured structures*Please refer to the usual webpage of our LogicGroup for more details and the abstract of the talk.

The seminar will be held remotely through Webex. Please write to luca.mottoros [at] unito [dot] itfor the link to the event.

The Cross-Alps Logic Seminar is co-organized by the logic groups of Genoa, Lausanne, Turin and Udine as part of our collaboration in the project PRIN 2017 'Mathematical logic: models, sets, computability'.

## This Week in Logic at CUNY

Logic and Metaphysics Workshop

Date: Monday, March 28, 4.15-6.15 (NY time), GC 5382

For meeting information (including zoom link for those wishing to attend remotely), please sign up for our mailing list at https://logic.commons.gc.cuny.edu/about/

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.

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, Universit`a degli Studi dell’Insubria.**

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

Title:** ****Toposes of Topological Monoid Actions.**

Abstract: Anyone encountering topos theory for the first time will be familiar with the fact that the category of actions of a monoid on sets is a special case of a presheaf topos. It turns out that if we equip the monoid with a topology and consider the subcategory of continuous actions, the result is still a Grothendieck topos. It is possible to characterize such toposes in terms of their points, and along the way extract canonical representing topological monoids, the complete monoids. I'll sketch the trajectory of this story, present some positive and negative results about Morita-equivalence of topological monoids, and explain how one can extract a semi-Galois theory from this set-up.

- - - - Thursday, Mar 31, 2022 - - - -

- - - - Friday, Apr 1, 2022 - - - -

Set Theory Seminar

CUNY Graduate Center, Friday, April 1, 12:30pm

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

Logic and Metaphysics Workshop

Date: Monday, April 4, 4.15-6.15 (NY time), GC 5382

For meeting information (including zoom link for those wishing to attend remotely), please sign up for our mailing list at https://logic.commons.gc.cuny.edu/about/

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.**

Title:** Enriched structure-semantics adjunctions and monad-theory equivalences for subcategories of arities.**

Abstract: Several structure-semantics adjunctions and monad-theory equivalences have been established in category theory. Lawvere (1963) developed a structure-semantics adjunction between Lawvere theories and tractable Set-valued functors, which was subsequently generalized by Linton (1969), while Dubuc (1970) established a structure-semantics adjunction between V-theories and tractable V-valued V-functors for a symmetric monoidal closed category V. It is also well known (and due to Linton) that there is an equivalence between Lawvere theories and finitary monads on Set. Generalizing this result, Lucyshyn-Wright (2016) established a monad-theory equivalence for eleutheric systems of arities in arbitrary closed categories. Building on earlier work by Nishizawa and Power, Bourke and Garner (2019) subsequently proved a general monad-theory equivalence for arbitrary small subcategories of arities in locally presentable enriched categories. However, neither of these equivalences generalizes the other, and there has not yet been a general treatment of enriched structure-semantics adjunctions that specializes to those established by Lawvere, Linton, and Dubuc.

Motivated by these considerations, we develop a general axiomatic framework for studying enriched structure-semantics adjunctions and monad-theory equivalences for subcategories of arities, which generalizes all of the aforementioned results and also provides substantial new examples of relevance for topology and differential geometry. For a subcategory of arities J in a V-category C over a symmetric monoidal closed category V, Linton’s notion of clone generalizes to provide enriched notions of J-theory and J-pretheory, which were also employed by Bourke and Garner (2019). We say that J is amenable if every J-theory admits free algebras, and is strongly amenable if every J-pretheory admits free algebras. If J is amenable, then we obtain an idempotent structure-semantics adjunction between certain J-pretheories and J-tractable V-categories over C, which yields an equivalence between J-theories and J-nervous V-monads on C. If J is strongly amenable, then we also obtain a rich theory of presentations for J-theories and J-nervous V-monads. We show that many previously studied subcategories of arities are (strongly) amenable, from which we recover the aforementioned structure-semantics adjunctions and monad-theory equivalences. We conclude with the result that any small subcategory of arities in a locally bounded closed category is strongly amenable, from which we obtain structure-semantics adjunctions and monad-theory equivalences in (e.g.) many convenient categories of spaces.

Joint work with Rory Lucyshyn-Wright.

- - - - Thursday, Apr 7, 2022 - - - -

- - - - Friday, Apr 8, 2022 - - - -

- - - - Other Logic News - - - -

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io

(site designed, built & maintained by Victoria Gitman)

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

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

## Kacper Kucharski, Using elementary submodels in topology

## Wednesday seminar

## Logic Seminar Wednesday 30 March 2022 16:00 hrs at NUS by Wu Liuzhen

## (KGRC) seminar talks Tuesday, March 29 and Thursday, March 31

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

## Correction to previous subject line

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

**Omer Ben-Neria**(The Hebrew University of Jerusalem)

will give a talk on

*Mathias-type Criterion for the Magidor Iteration of Prikry forcings*Please refer to the usual webpage of our LogicGroup for more details and the abstract of the talk.

The seminar will be held remotely through Webex. Please write to luca.mottoros [at] unito [dot] itfor the link to the event.

The Cross-Alps Logic Seminar is co-organized by the logic groups of Genoa, Lausanne, Turin and Udine as part of our collaboration in the project PRIN 2017 'Mathematical logic: models, sets, computability'.

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

## This Week in Logic at CUNY

Logic and Metaphysics Workshop

Date: Monday, March 21, 4.15-6.15 (NY time), GC 5382

For meeting information (including zoom link for those wishing to attend remotely), please sign up for our mailing list at https://logic.commons.gc.cuny.edu/about/

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.

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 - - - -

CUNY Graduate Center, Friday, March 25, 12:30pm

- - - - Monday, Mar 28, 2022 - - - -

Logic and Metaphysics Workshop

Date: Monday, March 28, 4.15-6.15 (NY time), GC 5382

For meeting information (including zoom link for those wishing to attend remotely), please sign up for our mailing list at https://logic.commons.gc.cuny.edu/about/

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.

- - - - 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, Universit`a degli Studi dell’Insubria.**

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

Title:** TBA.**

- - - - Thursday, Mar 31, 2022 - - - -

- - - - Friday, Apr 1, 2022 - - - -

Set Theory Seminar

CUNY Graduate Center, Friday, April 1, 12:30pm

- - - - Other Logic News - - - -

- - - - Web Site - - - -

"Find us on the web at: nylogic.github.io

(site designed, built & maintained by Victoria Gitman)"

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

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

## Kamil Ryduchowski, Elementary submodels and infinitary combinatorics

## (KGRC) Set Theory Research Seminar talk on Tuesday, March 22

## Wednesday seminar

## Logic seminar Tuesday March 22

## Logic Seminar 16 March 2022 16:00 hrs SGT by Leszek Kolodziejcyk, University of Warsaw

## Gruesse aus Singapur

## Cross-Alps Logic Seminar (speaker: Damir Dzhafarov)

**Damir Dzhafarov**(University of Connecticut)

will give a talk on

*The SRT22 vs. COH problem*Please refer to the usual webpage of our LogicGroup for more details and the abstract of the talk.

The seminar will be held remotely through Webex. Please write to luca.mottoros [at] unito [dot] itfor the link to the event.

The Cross-Alps Logic Seminar is co-organized by the logic groups of Genoa, Lausanne, Turin and Udine as part of our collaboration in the project PRIN 2017 'Mathematical logic: models, sets, computability'.

## This Week in Logic at CUNY

Logic and Metaphysics Workshop

Date: Monday, March 14, 4.15-6.15 (NY time), GC 5382

For meeting information (including zoom link for those wishing to attend remotely), please sign up for our mailing list at https://logic.commons.gc.cuny.edu/about/

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**

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 - - - -

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 - - - -

- - - - Monday, Mar 21, 2022 - - - -

Logic and Metaphysics Workshop

Date: Monday, March 21, 4.15-6.15 (NY time), GC 5382

For meeting information (including zoom link for those wishing to attend remotely), please sign up for our mailing list at https://logic.commons.gc.cuny.edu/about/

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.

- - - - 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 - - - -

CUNY Graduate Center, Friday, March 25, 12:30pm

- - - - Other Logic News - - - -

- - - - Web Site - - - -

"Find us on the web at: nylogic.github.io

(site designed, built & maintained by Victoria Gitman)"

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

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

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

## (KGRC) seminar talks Tuesday, March 15 and Thursday, March 17

## Wednesday seminar

## Logic Seminar 16 March 2022 17:00 hrs at NUS by Leszek Kolodziejczyk

## Logic Seminar 16 March 2022 17:00 hrs at NUS by Leszek Kolodziejczyk

## Cross-Alps Logic Seminar (speaker: Alessandro Andretta)

**Alessandro Andretta**(University of Turin)

will give a talk on

*Sierpinski’s partitions with Sigma^1_2 pieces*Please refer to the usual webpage of our LogicGroup for more details and the abstract of the talk.

The seminar will be held remotely through Webex. Please write to luca.mottoros [at] unito [dot] it for the link to the event.

The Cross-Alps Logic Seminar is co-organized by the logic groups of Genoa, Lausanne, Turin and Udine as part of our collaboration in the project PRIN 2017 'Mathematical logic: models, sets, computability'.

## This Week in Logic at CUNY

Logic and Metaphysics Workshop

Date: Monday, March 7, 4.15-6.15 (NY time), GC 5382

For meeting information (including zoom link for those wishing to attend remotely), please sign up for our mailing list at https://logic.commons.gc.cuny.edu/about/

David Papineau (King’s).

Title: Understanding Causal Inference

Abstract: The current pandemic has focused attention on the techniques used by epidemiologists and other non-experimental scientists to infer causal hypotheses from correlational data. These techniques, which hinge on assumptions about the way causal connections manifest themselves in conditional and unconditional correlations, pose an obvious philosophical challenge. What is it about causation that allows them to work? None of the mainstream accounts of causation—counterfactual, process, dispositional, regularity—casts any light on this question. Probabilistic and interventionist theories of causation do offer a direct response to the challenge, by positing a constitutive connection between causes and correlations, but I shall argue that these theories do not dig deep enough. Instead I shall develop an older idea—which goes back to H.A. Simon in the 1950s—that relates causal relationships to systems of structural equations with probabilistically independent exogenous variables. The attraction of this structural equations approach is that it allows us to view the correlational patterns as fallible evidence for causal relationships, rather than constitutive of them. I shall consider whether this approach can lead to a full reduction of causation and how it might accommodate quantum mechanical unpredictability.

- - - - Tuesday, Mar 8, 2022 - - - -

- - - - Wednesday, Mar 9, 2022 - - - -

- - - - Friday, Mar 11, 2022 - - - -

CUNY Graduate Center, Friday, March 11, 12:30pm

**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/

- - - - Monday, Mar 14, 2022 - - - -

Logic and Metaphysics Workshop

Date: Monday, March 14, 4.15-6.15 (NY time), GC 5382

For meeting information (including zoom link for those wishing to attend remotely), please sign up for our mailing list at https://logic.commons.gc.cuny.edu/about/

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

- - - - Wednesday, Mar 16, 2022 - - - -

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 - - - -

CUNY Graduate Center, Friday, March 18, 12:30pm

- - - - Other Logic News - - - -

- - - - Web Site - - - -

"Find us on the web at: nylogic.github.io

(site designed, built & maintained by Victoria Gitman)"

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

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

## CMU math logic seminar on Tuesday, March 15

## Wednesday seminar

## (KGRC) seminar talks Tuesday, March 8 and Thursday, March 10

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

On Friday 04.03.2022 at 16:00

**Michal Skrzypczak**(University of Warsaw)

will give a talk on

*The infinite tree - from Kolmogorov, Rabin, and Shelah to modern Theoretical Computer Science*Please refer to the usual webpage of our LogicGroup for more details and the abstract of the talk.

The seminar will be held remotely through Webex. Here are the information to access the meeting:

**ACCESS TO WEBEX MEETING**

Link Meeting

Number Meeting: 2733 686 2768

Password: ErDGYCdk795

The Cross-Alps Logic Seminar is co-organized by the logic groups of Genoa, Lausanne, Turin and Udine as part of our collaboration in the project PRIN 2017 'Mathematical logic: models, sets, computability'.

All the best,

Luca

--

We sent you this email because you are in the mailing list of Cross-Alps Logic Seminar.

If you do not want to receive our seminar announcements anymore, please write to luca.mottoros@unito.it.

## This Week in Logic at CUNY

Logic and Metaphysics Workshop

Date: Monday, February 28, 4.15-6.15 (NY time), GC 5382

For meeting information (including zoom link for those wishing to attend remotely), please sign up for our mailing list at https://logic.commons.gc.cuny.edu/about/

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 - - - -

CUNY Graduate Center, Friday, March 4, 12:30pm

**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.

- - - - Monday, Mar 7, 2022 - - - -

Logic and Metaphysics Workshop

Date: Monday, March 7, 4.15-6.15 (NY time), GC 5382

For meeting information (including zoom link for those wishing to attend remotely), please sign up for our mailing list at https://logic.commons.gc.cuny.edu/about/

David Papineau (King’s).

Title: Understanding Causal Inference

Abstract: The current pandemic has focused attention on the techniques used by epidemiologists and other non-experimental scientists to infer causal hypotheses from correlational data. These techniques, which hinge on assumptions about the way causal connections manifest themselves in conditional and unconditional correlations, pose an obvious philosophical challenge. What is it about causation that allows them to work? None of the mainstream accounts of causation—counterfactual, process, dispositional, regularity—casts any light on this question. Probabilistic and interventionist theories of causation do offer a direct response to the challenge, by positing a constitutive connection between causes and correlations, but I shall argue that these theories do not dig deep enough. Instead I shall develop an older idea—which goes back to H.A. Simon in the 1950s—that relates causal relationships to systems of structural equations with probabilistically independent exogenous variables. The attraction of this structural equations approach is that it allows us to view the correlational patterns as fallible evidence for causal relationships, rather than constitutive of them. I shall consider whether this approach can lead to a full reduction of causation and how it might accommodate quantum mechanical unpredictability.

- - - - Tuesday, Mar 8, 2022 - - - -

- - - - Wednesday, Mar 9, 2022 - - - -

The New York City Category Theory Seminar

Department of Computer Science

Department of Mathematics

The Graduate Center of The City University of New York

New URL: http://www.sci.brooklyn.cuny.edu/~noson/Seminar/index.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 - - - -

CUNY Graduate Center, Friday, March 11, 12:30pm

**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)"

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

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

## Wednesday seminar

## European Set Theory Conference: 29 August - 2 September 2022

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

## (KGRC) Set Theory Seminar talk on Tuesday, March 1

## Two CMU seminars next Tuesday

## This Week in Logic at CUNY

- - - - Tuesday, Feb 22, 2022 - - - -

- - - - Wednesday, Feb 23, 2022 - - - -

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)**

Date and Time: Wednesday February 23, 2022, 7:00 - 8:30 PM., on Zoom.

Title: Do you have what it takes to use the diagonal argument?

Abstract: Lawvere's reformulation of the diagonal argument captured many instances from the literature in an elegant and abstract category-theoretic treatment. The original version used cartesian closed categories, but gave a nod to how the statement of the argument could be adjusted so as to make fewer demands on the category. In fact the argument, and the fixed-point theorem that Lawvere provided as the positive version of the argument, both require much less than Lawvere stated. This talk will give an outline of Lawvere's version of the diagonal argument, his corresponding fixed-point theorem, and then cover a few versions obtained recently that drop assumptions on the properties/structure of the category at hand.

- - - - Thursday, Feb 24, 2022 - - - -

- - - - Friday, Feb 25, 2022 - - - -

CUNY Graduate Center, Friday, February 25, 12:30pm

As part of this, we shall see a failed attempt to find a proper class which is not big in the theory ZF without Power Set but with Collection - which is by taking a certain symmetric submodel of a class forcing. It will turn out that this approach fails because, unlike in the set forcing case, the symmetric submodel of a class forcing need not exhibit many of the nice properties that we would expect. Notably, Collection may fail and, in fact, it is unclear which axioms need necessarily hold.

This will lead to the definition of the 'Respected Model', an alternative approach to defining a submodel of a class forcing in which Choice fails. We will investigate the properties of this new model and compare it to the symmetric version.

Logic and Metaphysics Workshop

Date: Monday, February 28, 4.15-6.15 (NY time), GC 5382

For meeting information, please sign up for our mailing list at https://logic.commons.gc.cuny.edu/about/

Michael Burton (Yale).

Title: Paraconsistency with some detachment

Abstract: In this talk, a proof-of-concept logic is presented that is like first-order LP (the “logic of paradox”) except things behave classically within the scope of universal quantifiers. This logic’s material conditional does not, in general, detach, but much can be deduced with it. Structures for this logic are classical first-order structures equipped with a congruence relation, giving this logic a connection to Priest’s collapsing lemma for LP. Some possible improvements to this logic are then discussed. One of these involves separating classicality from universal quantification, having classicality be mediated instead by operators that interact with variable assignments. Finally, the relevance of logics of this kind to various logical paradoxes is discussed.

- - - - Tuesday, Mar 1, 2022 - - - -

- - - - Wednesday, Mar 2, 2022 - - - -

- - - - Thursday, Mar 3, 2022 - - - -

- - - - Friday, Mar 4, 2022 - - - -

CUNY Graduate Center, Friday, March 4, 12:30pm

- - - - Other Logic News - - - -

- - - - Web Site - - - -

"Find us on the web at: nylogic.github.io

(site designed, built & maintained by Victoria Gitman)"

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

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

## Next CMU math logic seminar

## Wednesday seminar

## Logic Seminar today at 16:30 hrs

## Wednesday seminar

## Logic Seminar Wed 16 February 2022 16:30 hrs by Rupert Hoelzl

## Logic Seminar Wed 16 February 2022 16:30 hrs by Rupert Hoelzl

## This Week in Logic at CUNY

- - - - Monday, Feb 14, 2022 - - - -

Logic and Metaphysics Workshop

Date: Monday, February 14, 4.15-6.15 (NY time), GC 5382

For meeting information, please sign up for our mailing list at https://logic.commons.gc.cuny.edu/about/

Ekaterina Kubyshkina (Campinas)

Title: Ignorance as an excuse, formally

Abstract: In the current literature on epistemology there is a lively debate on which type of ignorance may provide a moral excuse. A good candidate is the one in which an agent has never considered or thought about a true proposition p. From a logical perspective, it is usual to model situations involving ignorance by means of epistemic logic. However, no formal analysis was provided for ignorance as an excuse. First, we will argue that if ignorance is expressed via standard modalities of knowledge and belief, one is unable to represent ignorance as an excuse. Secondly, we fill this gap by providing an original logical setting for modelling this type of ignorance. In particular, we introduce a complete and sound logic in which ignorance is expressed as a primitive modality. Semantically, the logic is characterized by Kripke semantics with possibly incomplete worlds. Moreover, in order to consider the conditions of a possible change of an agent’s ignorance, we will extend the setting by considering public announcements.

- - - - Tuesday, Feb 15, 2022 - - - -

- - - - Wednesday, Feb 16, 2022 - - - -

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: Emilio Minichiello, CUNY Graduate Center.

Title: Category Theory ∩ Differential Geometry.

· Abstract: In this talk we will take a tour through some areas of math at the intersection of category theory and differential geometry. We will talk about how the use of category theory works towards solving 2 problems: 1) to give rigorous definitions and techniques to study increasingly complicated objects in differential geometry that are coming from physics, like orbifolds and bundle gerbes, and 2) to find good categories in which to embed the category of finite dimensional smooth manifolds, without losing too much geometric intuition. This involves the study of Lie groupoids, sheaves, diffeological spaces, stacks, and infinity stacks. I will try to motivate the use of these mathematical objects and how they help mathematicians understand differential geometry and expand its scope.

- - - - Thursday, Feb 17, 2022 - - - -

- - - - Friday, Feb 18, 2022 - - - -

CUNY Graduate Center, Friday, February 18, 12:30pm

**Sittinon Jirattikansakul**, Tel Aviv University**Forcing with overlapping supercompact extenders: Part II**

In the paper 'Blowing up the power of a singular cardinal of uncountable cofinality', Gitik introduced the forcing which can violate the SCH at singular cardinals of any cofinalities, assuming that the singular cardinals are also singular in the ground model. The forcing is built up from a Mitchell increasing sequence of strong extenders, and it preserves all cardinals and cofinalities in the generic extension. In this talk, we will discuss a forcing which is built from a Mitchell increasing sequence of supercompact extenders. The forcing also violates the SCH at singular cardinals of any cofinalities which are singular in the ground model. An important feature of this forcing is that it is possible to collapse the successor of a singular cardinal, while preserving cardinals above it.

- - - - Monday, Feb 21, 2022 - - - -

- - - - Tuesday, Feb 22, 2022 - - - -

- - - - Wednesday, Feb 23, 2022 - - - -

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)**

Date and Time: Wednesday February 23, 2022, 7:00 - 8:30 PM., on Zoom.

Title: Do you have what it takes to use the diagonal argument?

Abstract: Lawvere's reformulation of the diagonal argument captured many instances from the literature in an elegant and abstract category-theoretic treatment. The original version used cartesian closed categories, but gave a nod to how the statement of the argument could be adjusted so as to make fewer demands on the category. In fact the argument, and the fixed-point theorem that Lawvere provided as the positive version of the argument, both require much less than Lawvere stated. This talk will give an outline of Lawvere's version of the diagonal argument, his corresponding fixed-point theorem, and then cover a few versions obtained recently that drop assumptions on the properties/structure of the category at hand.

- - - - Thursday, Feb 24, 2022 - - - -

- - - - Friday, Feb 25, 2022 - - - -

CUNY Graduate Center, Friday, February 25, 12:30pm

- - - - Other Logic News - - - -

- - - - Web Site - - - -

"Find us on the web at: nylogic.github.io

(site designed, built & maintained by Victoria Gitman)"

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

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

## Next two CMU math logic seminars

## This Week in Logic at CUNY

- - - - Monday, Feb 7, 2022 - - - -

Logic and Metaphysics Workshop

Date: Monday, February 7, 4.15-6.15 (NY time), GC 5382

For meeting information, please sign up for our mailing list at https://logic.commons.gc.cuny.edu/about/

Title: Frame Definability in Finitely-Valued Modal Logics

Abstract: In this paper we study frame definability in finitely-valued modal logics and establish two main results via suitable translations: (1) in finitely-valued modal logics one cannot define more classes of frames than are already definable in classical modal logic, and (2) a large family of finitely-valued modal logics define exactly the same classes of frames as classical modal logic (including modal logics based on finite Heyting and MV-algebras). In this way one may observe, for example, that the celebrated Goldblatt–Thomason theorem applies immediately to these logics. In particular, we obtain the central result from [B. Teheux. Modal definability for Łukasiewicz validity relations. Studia Logica 104 (2): 343–363 (2016)] with a much simpler proof and answer one of the open questions left in that paper. Moreover, the proposed translations allow us to determine the computational complexity of a big class of finitely-valued modal logics.

Note: This is joint work with Carles Noguera and Xavier Caicedo.

- - - - Tuesday, Feb 8, 2022 - - - -

- - - - Wednesday, Feb 9, 2022 - - - -

- - - - Thursday, Feb 10, 2022 - - - -

- - - - Friday, Feb 11, 2022 - - - -

CUNY Graduate Center, Friday, February 11, 12:30pm

**Sittinon Jirattikansakul**, Tel Aviv University**Forcing with overlapping supercompact extenders**

In the paper 'Blowing up the power of a singular cardinal of uncountable cofinality', Gitik introduced the forcing which can violate the SCH at singular cardinals of any cofinalities, assuming that the singular cardinals are also singular in the ground model. The forcing is built up from a Mitchell increasing sequence of strong extenders, and it preserves all cardinals and cofinalities in the generic extension. In this talk, we will discuss a forcing which is built from a Mitchell increasing sequence of supercompact extenders. The forcing also violates the SCH at singular cardinals of any cofinalities which are singular in the ground model. An important feature of this forcing is that it is possible to collapse the successor of a singular cardinal, while preserving cardinals above it.

- - - - Monday, Feb 14, 2022 - - - -

Logic and Metaphysics Workshop

Date: Monday, February 14, 4.15-6.15 (NY time), GC 5382

For meeting information, please sign up for our mailing list at https://logic.commons.gc.cuny.edu/about/

Ekaterina Kubyshkina (Campinas)

Title: Ignorance as an excuse, formally

Abstract: In the current literature on epistemology there is a lively debate on which type of ignorance may provide a moral excuse. A good candidate is the one in which an agent has never considered or thought about a true proposition p. From a logical perspective, it is usual to model situations involving ignorance by means of epistemic logic. However, no formal analysis was provided for ignorance as an excuse. First, we will argue that if ignorance is expressed via standard modalities of knowledge and belief, one is unable to represent ignorance as an excuse. Secondly, we fill this gap by providing an original logical setting for modelling this type of ignorance. In particular, we introduce a complete and sound logic in which ignorance is expressed as a primitive modality. Semantically, the logic is characterized by Kripke semantics with possibly incomplete worlds. Moreover, in order to consider the conditions of a possible change of an agent’s ignorance, we will extend the setting by considering public announcements.

- - - - Tuesday, Feb 15, 2022 - - - -

- - - - Wednesday, Feb 16, 2022 - - - -

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: Emilio Minichiello, CUNY Graduate Center.

Title: Category Theory ∩ Differential Geometry.

· Abstract: In this talk we will take a tour through some areas of math at the intersection of category theory and differential geometry. We will talk about how the use of category theory works towards solving 2 problems: 1) to give rigorous definitions and techniques to study increasingly complicated objects in differential geometry that are coming from physics, like orbifolds and bundle gerbes, and 2) to find good categories in which to embed the category of finite dimensional smooth manifolds, without losing too much geometric intuition. This involves the study of Lie groupoids, sheaves, diffeological spaces, stacks, and infinity stacks. I will try to motivate the use of these mathematical objects and how they help mathematicians understand differential geometry and expand its scope.

- - - - Thursday, Feb 17, 2022 - - - -

- - - - Friday, Feb 18, 2022 - - - -

CUNY Graduate Center, Friday, February 18, 12:30pm

**Sittinon Jirattikansakul**, Tel Aviv University**Forcing with overlapping supercompact extenders: Part II**

In the paper 'Blowing up the power of a singular cardinal of uncountable cofinality', Gitik introduced the forcing which can violate the SCH at singular cardinals of any cofinalities, assuming that the singular cardinals are also singular in the ground model. The forcing is built up from a Mitchell increasing sequence of strong extenders, and it preserves all cardinals and cofinalities in the generic extension. In this talk, we will discuss a forcing which is built from a Mitchell increasing sequence of supercompact extenders. The forcing also violates the SCH at singular cardinals of any cofinalities which are singular in the ground model. An important feature of this forcing is that it is possible to collapse the successor of a singular cardinal, while preserving cardinals above it.

- - - - Other Logic News - - - -

- - - - Web Site - - - -

"Find us on the web at: nylogic.github.io

(site designed, built & maintained by Victoria Gitman)"

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## Logic Seminar Wed 9 Feb 2022 16:00 hrs at NUS by Xie Ruofei

## Wednesday seminar

## This Week in Logic at CUNY

- - - - Monday, Jan 31, 2022 - - - -

- - - - Tuesday, Feb 1, 2022 - - - -

- - - - Wednesday, Feb 02, 2022 - - - -

- - - - Thursday, Feb 03, 2022 - - - -

- - - - Friday, Feb 04, 2022 - - - -

Next Week in Logic at CUNY:

- - - - Monday, Feb 7, 2022 - - - -

Logic and Metaphysics Workshop

Date: Monday, February 7, 4.15-6.15 (NY time), GC 5382

For meeting information, please sign up for our mailing list at https://logic.commons.gc.cuny.edu/about/

Title: Frame Definability in Finitely-Valued Modal Logics

Abstract: In this paper we study frame definability in finitely-valued modal logics and establish two main results via suitable translations: (1) in finitely-valued modal logics one cannot define more classes of frames than are already definable in classical modal logic, and (2) a large family of finitely-valued modal logics define exactly the same classes of frames as classical modal logic (including modal logics based on finite Heyting and MV-algebras). In this way one may observe, for example, that the celebrated Goldblatt–Thomason theorem applies immediately to these logics. In particular, we obtain the central result from [B. Teheux. Modal definability for Łukasiewicz validity relations. Studia Logica 104 (2): 343–363 (2016)] with a much simpler proof and answer one of the open questions left in that paper. Moreover, the proposed translations allow us to determine the computational complexity of a big class of finitely-valued modal logics.

Note: This is joint work with Carles Noguera and Xavier Caicedo.

- - - - Tuesday, Feb 8, 2022 - - - -

- - - - Wednesday, Feb 9, 2022 - - - -

- - - - Thursday, Feb 10, 2022 - - - -

- - - - Friday, Feb 11, 2022 - - - -

CUNY Graduate Center, Friday, February 11, 2pm

**Sittinon Jirattikansakul**, Tel Aviv University**Forcing with overlapping supercompact extenders**

- - - - Other Logic News - - - -

- - - - Web Site - - - -

"Find us on the web at: nylogic.github.io

(site designed, built & maintained by Victoria Gitman)"

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

## Logic Seminar 3 February 2022 16:00 hrs at NUS by Andre Nies

## Barcelona Set Theory Seminar

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

## Logic Seminar 26 January 2022 16:00 hrs at NUS by Zhang Jing (today)

## Wednesday seminar

## (KGRC) video recording of Víctor Torres's talk

## (KGRC) Logic Colloquium talk on Thursday, January 27

## This Week in Logic at CUNY

- - - - Tuesday, Jan 18, 2022 - - - -

- - - - Wednesday, Jan 19, 2022 - - - -

- - - - Thursday, Jan 20, 2022 - - - -

- - - - Friday, Jan 21, 2022 - - - -

Set Theory Seminar

Wolfgang Wohofsky, University of Vienna

Distributivity spectrum and fresh functions: Part II

In the first talk, I will mainly focus on the notion of fresh functions and the corresponding spectrum. A function with domain lambda is fresh if it is new but all its initial segments are in the ground model. I will give general facts how to compute the fresh function spectrum, also discussing what sets are realizable as a fresh function spectrum of a forcing. Moreover, I will provide several examples, including well-known tree forcings on omega such as Sacks and Mathias forcing, as well as Prikry and Namba forcing to illustrate the difference between fresh functions and fresh subsets.

In the second talk, I will also discuss another ('combinatorial') distributivity spectrum; most importantly, analyzing this notion for the forcing P(omega)/fin.

This is joint work with Vera Fischer and Marlene Koelbing.

Next Week in Logic at CUNY:

- - - - Monday, Jan 24, 2022 - - - -

- - - - Tuesday, Jan 25, 2022 - - - -

- - - - Wednesday, Jan 26, 2022 - - - -

- - - - Thursday, Jan 27, 2022 - - - -

- - - - Friday, Jan 28, 2022 - - - -

- - - - Other Logic News - - - -

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io

(site designed, built & maintained by Victoria Gitman)

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

## (KGRC) Set Theory Seminar talk on Tuesday, January 18

## Wednesday seminar

## Logic Seminar Talk 19 Jan 2022 16:00 hrs at NUS over Zoom by Ye Jinhe

## World Logic Day Event // January 14

## (KGRC) (corrected) World Logic Day 2022

## Logic Day Special Wed 12 Jan 2022 16:00 hrs SGT

## Wednesday seminar

## 21.12.2021 Seminar canceled

## Damian Sobota, Measures with the Additive Property and the random forcing

## Wednesday seminar

## This Week in Logic at CUNY

Monday, December 13, 2pm

The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

On the principle of disjunctive correctness

The disjunctive correctness principle (DC) states that a disjunction of arbitrary (possibly nonstandard) length is true if and only if one of its disjuncts is true. On first sight, the principle seems an innocent and natural generalization of the familiar compositional truth axiom for disjunction. However, Ali Enayat and Fedor Pakhomov demonstrated that (DC) has the same strength as Delta_0 induction, hence it produces a non-conservative extension of the background arithmetical theory.

In the presentation the proof of a stronger result will be presented. Let (DC-Elim) be just one direction of (DC), namely, the implication 'if a disjunction is true, then one of it disjuncts is true'. We will show that already (DC-Elim) carries the full strength of Delta_0 induction; moreover, the proof of this fact will be significantly simpler than the original argument of Enayat and Pakhomov.

Date: Monday, December 13th, 4.15-6.15 (NY time)

For meeting information, please sign up for our mailing list at https://logic.commons.gc.cuny.edu/about/

Title: Singular existentials and three different kinds of negation

Abstract: In this paper, I will argue for a new semantic analysis of (i) singular existential and (ii) atomic sentences to be able to cover three possible types of negation of them. Firstly, I will show that all three negations of sentences of kind (i) are equivalent if we make use of referring or non-referring names, while on the other hand the three negations of sentences of kind (ii) have several non-equivalent readings if non- referring names are used. Secondly, I will review the partial solutions to our problem given by Russell, Quine and Sainsbury and show in how far they fail. Thirdly, I will propose an alternative solution based on a semantics outlined in Rami (2020). Finally, I will show that we must distinguish two types of negation and that a unification in both directions fails.

- - - - Tuesday, Dec 14, 2021 - - - -

Computational Logic seminar

Contact sartemov@gc.cuny.edu for a zoom link

Speaker: V. Alexis Peluce, CUNY Graduate Center

Title: Explicit Modal Logic as the Structure of Relevance

Abstract. Orlov and Gödel pioneered the method of syntactic translation of propositional formulas into modal language. Justification Logic takes this a step further by revealing the explicit content of individual modalities. Sergei Artemov extended Gödel's work by showing that S4 can be interpreted in the Logic of Proofs, which can in turn be interpreted in terms of arithmetical proof predicates, thereby providing a rigorous arithmetical foundation for constructivism.

In this work, we examine Classical Logic through the Gödel-Artemov lens. The paradoxes of material implication are a family of classical implications that diverge in meaning from the natural language conditional. We present seven such paradoxes, translate them into S5|the natural modal counterpart of CPC|and then populate the resulting S5 formulas with explicit modalities. We show that for each of our paradoxes, there is a corresponding explicit, non-paradoxical formula. This, we suggest, provides a general method for solving the paradoxes of material implication.

- - - - Wednesday, Dec 15, 2021 - - - -

Department of Computer Science

Department of Mathematics

The Graduate Center of The City University of New York

Date and Time: Wednesday December 15, 2021, 7:00 - 8:30 PM., on Zoom (contact noson@sci.brooklyn.cuny.edu for the link)

- - - - Thursday, Dec 16, 2021 - - - -

- - - - Friday, Dec 17, 2021 - - - -

- - - - Monday, Dec 20, 2021 - - - -

- - - - Tuesday, Dec 21, 2021 - - - -

- - - - Wednesday, Dec 22, 2021 - - - -

- - - - Thursday, Dec 23, 2021 - - - -

- - - - Friday, Dec 24, 2021 - - - -

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io

(site designed, built & maintained by Victoria Gitman)

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## Agnieszka Widz, Magic Sets

## Barcelona Set Theory Seminar

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

## (KGRC) four talks on Tuesday, December 14 and one talk on Thursday, December 16

## Mirna Dzamonja @ Toronto Set Theory Seminar

## This Week in Logic at CUNY

- - - - Monday, Dec 6, 2021 - - - -

Monday, December 6, 2pm

The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Bartosz Wcisło, Polish Academy of Sciences**Model theoretic characterizations of truth: Part II**

This is joint work (still in progress) with Mateusz Łełyk (who gave the first part of the talk). By an axiomatic theory of truth (for the language of arithmetic, ) we mean a theory in L enriched with a fresh unary predicate which (extends the elementary arithmetic EA and) proves all sentences of the form ( being a sentence in L)

The collection of all sentence of the above form is normally called . It is well known that axiomatic theories of truth have a number of interesting model-theoretic consequences. For example, already relatively weak theories of truth impose recursive saturation, in the sense that the L-reduct of any model of such theory is recursively saturated. To give another example, already imposes elementary equivalence of models, in the sense that whenever , , and (the first model is a submodel of the second one), then actually and are elementarily equivalent. During (both parts) of the talk we investigate which of these properties actually characterize the respective truth theory up to definability. In particular, in the first part of the talk, we prove the following results (we restrict ourselves to theories in a finite language and extending EA):

- Every theory which imposes elementary equivalence defines .
- Every theory which imposes full elementarity defines .

Additionally, we take a look at the definability relations between axiomatic truth theories and axiomatic theories of definability or skolem functions.

Date: Monday, December 6th, 4.15-6.15 (NY time)

For meeting information, please sign up for our mailing list at https://logic.commons.gc.cuny.edu/about/

Title: Every Logic has its Proper Semantics

Abstract: Many logics are sound and complete with respect to a multiplicity of semantic systems. These assign different sets of models to the logic. It will be shown that a series of problems result if all these semantic systems are on a par. I shall present a method to define a unique ‘proper’ semantics for the members of a huge class of logics, containing all usual deductive logics, and argue (i) that the proper semantics is defined in terms of syntactic criteria and so depends fully on the logic, (ii) that there are philosophical arguments to consider a logic’s proper semantics as natural, for example it correctly describes the ‘situations’ that are possible according to the logic. This solves the problems mentioned previously. Implications for the discussion on inferentialism are obvious. For some logics, the proper semantics coincides with the Henkin semantics. For other logics L, the proper semantics counts more models than the Henkin semantics: moreover, not all Henkin models are maximally L-non-trivial. A small change to the Henkin method has the effect that, for every logic L, the Henkin semantics coincides with the proper semantics.

- - - - Tuesday, Dec 7, 2021 - - - -

- - - - Wednesday, Dec 8, 2021 - - - -

The New York City Category Theory Seminar

Department of Computer Science

Department of Mathematics

The Graduate Center of The City University of New York

Date and Time: Wednesday December 8, 2021, 7:00 - 8:30 PM., on Zoom (contact noson@sci.brooklyn.cuny.edu for the link)

Title: Toposes of presheaves on a monoid and their points.

Abstract: In 2014, Connes and Consani constructed their Arithmetic Site, with as underlying topos the topos of presheaves on the monoid of nonzero natural numbers under multiplication. One of their surprising results is that the points of this topos are classified by a double quotient of the finite adeles, leading immediately to a link with number theory. Inspired by this, we will consider toposes of presheaves on various monoids, and discuss strategies of calculating their points. The most recent strategies (involving for example étale geometric morphisms and complete spreads) are based on joint work with Morgan Rogers.

- - - - Thursday, Dec 9, 2021 - - - -

- - - - Friday, Dec 10, 2021 - - - -

https://philog.arthurpaulpedersen.org/

"What is Information and How to Measure it?"

Abstract: In view of the duality between subsets and quotient sets (= partitions = equivalence relations), the Boolean logic of subsets (usually presented as "propositional" logic) has a dual logic of partitions. The quantitative version of Boolean logic is the Boole-Laplace notion of logical probability. Gian-Carlo Rota held that probability is to subsets as information is to partitions, so the quantitative version of partition logic is the theory of logical entropy. This talk is an introduction to logical entropy as the natural measure (in the sense of measure theory) of information as distinctions. It is also shown that the Shannon entropy (which is not a measure) is a uniform transform of logical entropy that is a different quantification of the same notion of information as distinctions.

CUNY Graduate Center, Room 6417

Friday, December 10, 2pm

Eyal Kaplan, Tel Aviv University**Non-stationary support iterations of Prikry forcings and restrictions of ultrapower embeddings to the ground model, part II**

Assume that is a forcing notion, is a generic set for it over the ground model , and a cardinal is measurable in the generic extension. Let be an ultrapower embedding, taken in with a normal measure on . We consider the following questions:

1. Is the restriction of to an iterated ultrapower of (by its measures or extenders)?

2. Is the restriction of to definable in ?

By a work of Schindler [1], the answer to the first question is affirmative, assuming that there is no inner model with a Woodin Cardinal and is the core model. By a work of Hamkins [2], the answer to the second question is positive for forcing notions which admit a Gap below .

We will address the above questions in the context of nonstationary-support iteration of Prikry forcings below a measurable cardinal . Assuming GCH only in the ground model, we provide a positive answer for the first question, and describe in detail the structure of restricted to as an iteration of . The answer to the second question may go either way, depending on the choice of the measures used in the Prikry forcings along the iteration; we will provide a simple sufficient condition for the positive answer. This is a joint work with Moti Gitik.

[1] Ralf Schindler. Iterates of the core model. Journal of Symbolic Logic, pages 241–251, 2006.

[2] Joel David Hamkins. Gap forcing. Israel Journal of Mathematics, 125(1):237–252, 2001.

- - - - Monday, Dec 13, 2021 - - - -

Monday, December 6, 2pm

The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

On the principle of disjunctive correctness

The disjunctive correctness principle (DC) states that a disjunction of arbitrary (possibly nonstandard) length is true if and only if one of its disjuncts is true. On first sight, the principle seems an innocent and natural generalization of the familiar compositional truth axiom for disjunction. However, Ali Enayat and Fedor Pakhomov demonstrated that (DC) has the same strength as Delta_0 induction, hence it produces a non-conservative extension of the background arithmetical theory.

In the presentation the proof of a stronger result will be presented. Let (DC-Elim) be just one direction of (DC), namely, the implication 'if a disjunction is true, then one of it disjuncts is true'. We will show that already (DC-Elim) carries the full strength of Delta_0 induction; moreover, the proof of this fact will be significantly simpler than the original argument of Enayat and Pakhomov.

Date: Monday, December 13th, 4.15-6.15 (NY time)

For meeting information, please sign up for our mailing list at https://logic.commons.gc.cuny.edu/about/

Title: Singular existentials and three different kinds of negation

Abstract: In this paper, I will argue for a new semantic analysis of (i) singular existential and (ii) atomic sentences to be able to cover three possible types of negation of them. Firstly, I will show that all three negations of sentences of kind (i) are equivalent if we make use of referring or non-referring names, while on the other hand the three negations of sentences of kind (ii) have several non-equivalent readings if non- referring names are used. Secondly, I will review the partial solutions to our problem given by Russell, Quine and Sainsbury and show in how far they fail. Thirdly, I will propose an alternative solution based on a semantics outlined in Rami (2020). Finally, I will show that we must distinguish two types of negation and that a unification in both directions fails.

- - - - Tuesday, Dec 14, 2021 - - - -

- - - - Wednesday, Dec 15, 2021 - - - -

Department of Computer Science

Department of Mathematics

The Graduate Center of The City University of New York

Date and Time: Wednesday December 15, 2021, 7:00 - 8:30 PM., on Zoom (contact noson@sci.brooklyn.cuny.edu for the link)

- - - - Thursday, Dec 16, 2021 - - - -

- - - - Friday, Dec 17, 2021 - - - -

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io

(site designed, built & maintained by Victoria Gitman)

-------- ADMINISTRIVIA --------

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

## Kacper Kucharski, Overcomplete sets in selected nonseparable Banach spaces

## Barcelona Set Theory Seminar

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

## (KGRC) Set Theory Research Seminar talk on Tuesday, December 7

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

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

## Barcelona Set Theory Seminar

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

## (KGRC) seminar talks on Tuesday, November 30 and Thursday, December 2

## Wednesday seminar

## Toronto Set Theory Seminar

## Barcelona Set Theory Seminar

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

## (KGRC) Set Theory Research Seminar talk on Tuesday, November 23

## Wednesday seminar

## Toronto Set Theory Seminar

## 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

Date: Tomorrow, Monday, November 15th, 4.15-6.15 (NY time)

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)

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)

- - - - Thursday, Nov 18, 2021 - - - -

- - - - Friday, Nov 19, 2021 - - - -

CUNY Graduate Center, Room 6417

Friday, November 19, 2pm

**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.

- - - - 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.

Date: Tomorrow, Monday, November 22th, 4.15-6.15 (NY time)

For meeting information, please sign up for our mailing list at https://logic.commons.gc.cuny.edu/about/

Konstantinos Georgatos (John Jay).

Title: Similarity through indistinguishability: the geodesic reasoning on Kripke models

Abstract: Several logical operators, such as conditionals, revision, and merge, are often understood through the selection of most similar worlds. In applications, similarity is expressed with distance and “most similar” translates to “closest” using a distance metric. We shall argue that similarity may arise through an indistinguishability relation between possible worlds and employ the geodesic distance of such a model to measure closeness. This understanding allows us to define a variety of operators that correspond to merging and revising. I will present a few systems and representation results and will show that revision, merging, and conditioning are interdefinable thus, in effect, satisfying the Ramsey test.

- - - - Tuesday, Nov 23, 2021 - - - -

- - - - Wednesday, Nov 24, 2021 - - - -

- - - - Thursday, Nov 25, 2021 - - - -

- - - - Friday, Nov 26, 2021 - - - -

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io

(site designed, built & maintained by Victoria Gitman)

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## Kamil Ryduchowski; An antiramsey coloring of pairs

## (KGRC) seminar talks Tuesday, November 16 and Thursday, November 18

## Two talks next Tuesday

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

## This Week in Logic at CUNY

Logic and Metaphysics Workshop

Date: Tomorrow, Monday, November 8th, 4.15-6.15 (NY time)

Speaker: Roman Kossak (CUNY GC)

Abstract: Almost any set of natural numbers you can think of is first-order definable in the standard model of arithmetic. A notable exception is the set Tr of Gödel numbers of true first-order sentences about addition and multiplication. On the one hand—by Tarski’s undefinability of truth theorem—Tr has no first order definition in the standard model; on the other, it has a straightforward definition in the form of an infinite disjunction of first order formulas. It is definable in a very mild extension of first-order logic. In 1963, Abraham Robinson initiated the study of possible truth assignments for sentences in languages represented in nonstandard models of arithmetic. Such assignments exist, but only in very special models; moreover they are highly non-unique, and—unlike Tr—they are not definable any reasonable formal system. In the talk, I will explain some model theory behind all that and I will talk about some recent results in the study of axiomatic theories of truth.

- - - - Tuesday, Nov 9, 2021 - - - -

Computational Logic Seminar

Tuesday November 9, 2021, 2-4pm,
Eastern Time US

For a zoom link, contact Sergei Artemov (sartemov@gc.cuny.edu)

**Tuesday November 9, 2021.**

Tuesday November 9, 2021, 2-4pm, Eastern Time US

For a zoom link, contact Sergei Artemov (sartemov@gc.cuny.edu)

**Tuesday November 9, 2021.**

**Speaker:**Antonis Achilleos, Reykjavik University

**Title:**Adventures in Monitorability

**Abstract:**

- - - - Wednesday, Nov 10, 2021 - - - -

- - - - Thursday, Nov 11, 2021 - - - -

- - - - Friday, Nov 12, 2021 - - - -

CUNY Graduate Center, Room 6417

Friday, November 12, 1pm

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.

- - - - 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)

- - - - Thursday, Nov 18, 2021 - - - -

- - - - Friday, Nov 19, 2021 - - - -

CUNY Graduate Center, Room 6417

Friday, November 19, 2pm

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io

(site designed, built & maintained by Victoria Gitman)

-------- ADMINISTRIVIA --------

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