## Set theory and toplogy seminar 16.04.2024 Krzysztof Zakrzewski (UW)

**(Wrocław University of Science and Technology) the lecture:**

**Krzysztof Zakrzewski (MIM UW)**

## Wednesday seminar

## Two Related Seminars in Geometry and Topology by Shlpak Banerjee and in Logic by Philipp Kunde on Wednesday 17 April 2024

## This Week in Logic at CUNY

Rutgers Logic Seminar

Monday Apr 8, Hill Center, Hill 705, SPECIAL TIME: 4:00pm

Jing Zhang, Toronto

Squares, ultrafilters and forcing axioms

Logic and Metaphysics Workshop

Date: Monday, April 8, 4.15-6.15pm (NY time)

Room: Graduate Center Room 7395

Title: Social construction and meta-ground

Abstract: The notion of social construction plays an important role in many areas of social philosophy, including the philosophy of gender, the philosophy of race, and social ontology. But it is far from clear how this notion (or cluster of notions) is to be understood. One promising proposal, which has been championed in recent years by Aaron Griffith (2017, 2018) and Jonathan Schaffer (2017), is that the notion of constitutive social construction may be analyzed in terms of the notion of metaphysical grounding. In this paper, I argue that a simple ground-theoretic analysis of social construction is subject to two sorts of problem cases and that existing ground-theoretic accounts do not avoid these problems. I then develop a novel ground-theoretic account of social construction in terms of meta-ground, and I argue that it avoids the problems. The core idea of the account is that in cases of social construction, the meta-ground of the relevant grounding fact includes a suitable connective social fact.

- - - - Tuesday, Apr 9, 2024 - - - -

MOPA (Models of Peano Arithmetic)

CUNY Graduate Center

Virtual (email Victoria Gitman for meeting id)

Tuesday, April 9, 1pm

Athar Abdul-Quader, Purchase College

Representations of lattices

- - - - Wednesday, Apr 10, 2024 - - - -

Department of Computer Science

Department of Mathematics

The Graduate Center of The City University of New York

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

Date and Time: Wednesday April 10, 2024, 7:00 - 8:30 PM. IN-PERSON

Title: Pulse Diagrams and Category Theory.

Abstract: ``Pulse diagrams'' are motivated by the ubiquity of pulsation in biology, from action potentials, to heartbeat, to respiration, and at longer time-scales to circadian rhythms and even to human behavior. The syntax of the diagrams is simple, and the semantics are easy to define and simulate with Python code. They express behaviors of parts and wholes as in categorical mereology, but are missing a compositional framework, like string diagrams. Examples to discuss include cellular automata, leaky-integrate-and-fire neurons, harmonic frequency generation, Gillespie algorithm for the chemical master equation, piecewise-linear genetic regulatory networks, Lotka-Volterra systems, and if time permits, aspects of the adaptive immune system. The talk is more about questions than about answers.

- - - - Thursday, Apr 11, 2024 - - - -

- - - - Friday, Apr 12, 2024 - - - -

CUNY Graduate Center

Friday, April 12, 12:30pm NY time

Virtual: Please email Victoria Gitman (vgitman@gmail.com) for meeting id.

Boban Velickovic University of Paris

Logic Workshop

CUNY Graduate Center

Friday April 12, 2:00pm-3:30pm, Room 5417

**Hans Schoutens**, CUNY**Geometric tools for the decidability of the existential theory of **

I will give a brief survey how tools from algebraic geometry can be used in finding solutions to Diophantine equations over and similar rings. These tools include Artin approximation, arc spaces, motives and resolution of singularities. This approach yields the definability of the existential theory of (in the ring language with a constant for ) contingent upon the validity of resolution of singularities (Denef-Schoutens). Anscombe-Fehm proved a weaker result using model-theoretic tools and together with Dittmann, they gave a proof assuming only the weaker 'local uniformization conjecture.'

- - - - Monday, Apr 15, 2024 - - - -

Rutgers Logic Seminar

Monday Apr 15, 3:30pm Hill Center, Hill 705

Logic and Metaphysics Workshop

Date: Monday, April 15, 4.15-6.15pm (NY time)

Room: Graduate Center Room 7395

Title: Imaging is Alpha + Aizerman

Abstract: I give a non-probabilistic account of the imaging revision process. Most familiar in its various probabilistic forms, imaging was introduced by David Lewis (1976) as the form of belief revision appropriate for supposing subjunctively that a hypothesis be true. It has played a central role in the semantics of subjunctive conditionals, in causal decision theory, and, less well known to philosophers, in the computational theory of information retrieval. In the economics literature, non-probabilistic imaging functions have been called “pseudo-rationalizable choice functions”. I show that the imaging functions are precisely those which satisfy both Sen’s Alpha Principle (aka “Chernoff’s Axiom”) and the Aizerman Axiom. This result allows us to see very clearly the formal relationship between non-probabilistic imaging and AGM revision (which is Alpha + Beta).

- - - - Tuesday, Apr 16, 2024 - - - -

- - - - Wednesday, Apr 17, 2024 - - - -

- - - - Thursday, Apr 18, 2024 - - - -

- - - - Friday, Apr 19, 2024 - - - -

CUNY Graduate Center

Friday April 19, 2:00pm-3:30pm, Room 5417

Some applications of model theory to lattice-ordered groups

When does a hyperarchimedean lattice-ordered group embed into a hyperarchimedean lattice-ordered group with strong unit? After explaining the meaning of this question, I will describe some partial answers obtained via model theory.

Speakers:

Paul Baginski (Fairfield)

Artem Chernikov (Maryland)

Alf Dolich (CUNY)

Alexei Kolesnikov (Towson)

NEMTD 2024 sponsored by the Mid-Atlantic Mathematical Logic Seminar (NSF grant #DMS-1834219) and the Wesleyan Department of Mathematics and Computer Science.

Organizers: Alex Kruckman, Rehana Patel, Alex Van Abel. Contact akruckman@wesleyan.edu with any questions.

## Logic Seminar Tuesday 9 April 2023 by Piotr Kowalski

## KGRC Talk - April 11

## Nankai Logic Colloquium paused for two weeks

## Set theory and topology seminar 9.04.2024 Jakub Rondos

**(Wrocław University of Science and Technology) the lecture:**

**Jakub Rondos (University of Vienna)**

(on behalf of the organizers, i.e. Piotr Borodulin-Nadzieja, Paweł Krupski, Aleksandra Kwiatkowska, Grzegorz Plebanek, Robert Rałowski and myself)

About 15 minutes before the seminar we invite you for coffee and a chat to social room A.4.1.A in C-19.

https://settheory.pwr.edu.pl/

http://www.math.uni.wroc.pl/seminarium/topologia

## Cross-Alps Logic Seminar (speaker: Luca Motto Ros)

**Luca Motto Ros**(University of Torino)

*Borel complexity of graph homomorphism*## This Week in Logic at CUNY

Logic and Metaphysics Workshop

Date: Monday, April 1, 4.15-6.15pm (NY time)

Room: Graduate Center Room 7395

Andrew Tedder (Vienna).

Title: Relevant logics as topical logics

Abstract: There is a simple way of reading a structure of topics into the matrix models of a given logic, namely by taking the topics of a given matrix model to be represented by subalgebras of the algebra reduct of the matrix, and then considering assignments of subalgebras to formulas. The resulting topic-enriched matrix models bear suggestive similarities to the two-component frame models developed by Berto et. al. in Topics of Thought. In this talk I’ll show how this reading of topics can be applied to the relevant logic R, and its algebraic characterisation in terms of De Morgan monoids, and indicate how we can, using this machinery and the fact that R satisfies the variable sharing property, read R as a topic-sensitive logic. I’ll then suggest how this approach to modeling topics can be applied to a broader range of logics/classes of matrices, and gesture at some avenues of research.

- - - - Tuesday, Apr 2, 2024 - - - -

MOPA (Models of Peano Arithmetic)

CUNY Graduate Center

Virtual (email Victoria Gitman for meeting id)

Tuesday, April 2, 1pm

**Athar Abdul-Quader**, Purchase College**Representations of lattices**

Following up on the series of talks on the history of the problem, in this talk we will discuss the main technique for realizing finite lattices as interstructure lattices, due to Schmerl in 1986. We will motivate this technique by studying an example: the Boolean algebra . We will see how we can modify the technique to produce elementary extensions realizing specific ranked lattices to ensure that such extensions are end, cofinal, or mixed extensions.

**Computational Logic Seminar**

**Spring 2024**

**(online)**

**Tuesday, April 2,**

**Time 2:00 - 4:00 PM**

**Speaker:**

**Sonja J.L. Smets**, The University of Amsterdam

**Title:**

*Reasoning about Epistemic Superiority and Data Exchange*

**Abstract:**In this presentation I focus on a framework that generalizes dynamic epistemic logic in order to model a wider range of scenarios including those in which agents read or communicate (or somehow gain access to) all the information stored at specific sources, or possessed by some other agents (including information of a non-propositional nature, such as data, passwords, secrets etc). The resulting framework allows one to reason about the state of affairs in which one agent (or group of agents) has ‘epistemic superiority’ over another agent (or group). I will present different examples of epistemic superiority and I will draw a connection to the logic of functional dependence by A. Baltag and J. van Benthem. At the level of group attitudes, I will further introduce the new concept of 'common distributed knowledge', which combines features of both common knowledge and distributed knowledge. This presentation is based on joint work with A. Baltag in [1].

[1] A. Baltag and S. Smets, Learning what others know, in L. Kovacs and E. Albert (eds.), LPAR23 proceedings of the International Conference on Logic for Programming, AI and Reasoning, EPiC Series in Computing, 73:90-110, 2020. https://doi.org/10.29007/plm4

- - - - Wednesday, Apr 3, 2024 - - - -

- - - - Thursday, Apr 4, 2024 - - - -

- - - - Friday, Apr 5, 2024 - - - -

April 5, Friday, 10 AM

Zoom meeting, please contact Rohit Parikh for zoom link

*The implicative conditional*, by Eric Raidl and myself, recently published in

*Journal of Philosophical Logic*(with free access). The paper presents a proposal for a strong conditional, that is, one that really expresses that the consequent is a consequence of the antecedent, or that the antecedent is a sufficient reason for believing the consequent, in a given context. We claim that the implicative conditional describes the logical behavior of an empirically defined class of natural language conditionals, also named implicative conditionals, which excludes concessive and some other conditionals. The logical properties of this conditional in a reflexive normal Kripke semantics will be discussed. Its axiomatic system, which was proved sound and complete, will be presented. The implicative conditional avoids the paradoxes of the material and strict conditionals, presents connexive properties, and assures the relevance of the antecedent to the consequent.

CUNY Graduate Center

Friday, April 5, 12:30pm NY time

Virtual: Please email Victoria Gitman (vgitman@gmail.com) for meeting id.

Kameryn Williams Bard College at Simon's Rock

Logic Workshop

CUNY Graduate Center

Friday April 5, 2:00pm-3:30pm, Room 5417

Decision problem for groups as equivalence relations

In 1911, Dehn proposed three decision problems for finitely presented groups: the word problem, the conjugacy problem, and the isomorphism problem. These problems have been central to both group theory and logic, and were each proven to be undecidable in the 50's. There is much current research studying the decidability of these problems in certain classes of groups.

Classically, when a decision problem is undecidable, its complexity is measured using Turing reducibility. However, Dehn's problems can also be naturally thought of as computably enumerable equivalence relations (ceers). We take this point of view and measure their complexity using computable reductions. This yields behaviors different from the classical context: for instance, every Turing degree contains a word problem, but not every ceer degree does. This leads us to study the structure of ceer degrees containing a word problem and other related questions.

- - - - Monday, Apr 8, 2024 - - - -

Rutgers Logic Seminar

Monday Apr 8, 3:30pm, Hill Center, Hill 705

Jing Zhang

Logic and Metaphysics Workshop

Date: Monday, April 8, 4.15-6.15pm (NY time)

Room: Graduate Center Room 7395

Title: Social construction and meta-ground

Abstract: The notion of social construction plays an important role in many areas of social philosophy, including the philosophy of gender, the philosophy of race, and social ontology. But it is far from clear how this notion (or cluster of notions) is to be understood. One promising proposal, which has been championed in recent years by Aaron Griffith (2017, 2018) and Jonathan Schaffer (2017), is that the notion of constitutive social construction may be analyzed in terms of the notion of metaphysical grounding. In this paper, I argue that a simple ground-theoretic analysis of social construction is subject to two sorts of problem cases and that existing ground-theoretic accounts do not avoid these problems. I then develop a novel ground-theoretic account of social construction in terms of meta-ground, and I argue that it avoids the problems. The core idea of the account is that in cases of social construction, the meta-ground of the relevant grounding fact includes a suitable connective social fact.

- - - - Tuesday, Apr 9, 2024 - - - -

- - - - Wednesday, Apr 10, 2024 - - - -

- - - - Thursday, Apr 11, 2024 - - - -

- - - - Friday, Apr 12, 2024 - - - -

CUNY Graduate Center

Friday, April 12, 12:30pm NY time

Virtual: Please email Victoria Gitman (vgitman@gmail.com) for meeting id.

Boban Velickovic University of Paris

Logic Workshop

CUNY Graduate Center

Friday April 12, 2:00pm-3:30pm, Room 5417

**Hans Schoutens**, CUNY**Geometric tools for the decidability of the existential theory of **

I will give a brief survey how tools from algebraic geometry can be used in finding solutions to Diophantine equations over and similar rings. These tools include Artin approximation, arc spaces, motives and resolution of singularities. This approach yields the definability of the existential theory of (in the ring language with a constant for ) contingent upon the validity of resolution of singularities (Denef-Schoutens). Anscombe-Fehm proved a weaker result using model-theoretic tools and together with Dittmann, they gave a proof assuming only the weaker 'local uniformization conjecture.'

Speakers:

Paul Baginski (Fairfield)

Artem Chernikov (Maryland)

Alf Dolich (CUNY)

Alexei Kolesnikov (Towson)

NEMTD 2024 sponsored by the Mid-Atlantic Mathematical Logic Seminar (NSF grant #DMS-1834219) and the Wesleyan Department of Mathematics and Computer Science.

Organizers: Alex Kruckman, Rehana Patel, Alex Van Abel. Contact akruckman@wesleyan.edu with any questions.

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

(site designed, built & maintained by Victoria Gitman)

## Wednesday seminar

## 49th Nankai Logic Colloquium

Hello everyone,

This week our weekly Nankai Logic Colloquium is going to be in the afternoon.

This is going to be an online event. Follow the link below to join the Zoom meeting. Please use your real name to join the meeting.

Title ：The 49th Nankai Logic Colloquium -- Aristotelis Panagiotopoulos

Time ：16:00pm, Mar. 29, 2024(Beijing Time)

Zoom Number ： 734 242 5443

Passcode ：477893

The records of past talks can be accessed at https://space.bilibili.com/253421893.

Best wishes,

Ming Xiao

## Logic Seminar Talks 27 March 2024 and 3 April 2024 at NUS

## UPDATE: This Week in Logic at CUNY

Rutgers Logic Seminar

Monday Mar 25, 3:30pm, Hill Center, Hill 705

Date: Monday, March 25, 4.15-6.15pm (NY time)

Room: Graduate Center Room 7395

Title: A moderate theory of overall resemblance

Abstract: This paper defends the moderate theory of overall resemblance stated by: A) y is at least as similar to x as z is iff: i) every resemblance property shared by x and z is also shared by x and y, and ii) for any resemblance family of properties F, y is at least as similar to x as z is with respect to F. In this account, a resemblance property is a property that corresponds to a genuine respect in which two things can resemble each other, whereas a resemblance family is a set of properties with respect to which things can be more or less similar to each other. An example of a resemblance property is being cubical, an example of a non-resemblance property is being either a gold cube or a silver sphere, and an example of a resemblance family is the set of specific mass properties.

- - - - Tuesday, Mar 26, 2024 - - - -

MOPA (Models of Peano Arithmetic)

CUNY Graduate Center

Virtual (email Victoria Gitman for meeting id)

Tuesday, March 26, 1pm

Roman Kossak, CUNY**The lattice problem for models of PA: Part ii**

The lattice problem for models of PA is to determine which lattices can be represented either as lattices of elementary substructures of a model of PA or, more generally, which can be represented as lattices of elementary substructures of a model N that contain a given elementary substructure M of N. I will talk about the history of the problem, from the seminal paper of Haim Gaifman from 1976 and other early results to some recent work of Jim Schmerl. There is much to talk about.

Computational Logic Seminar

Spring 2024 (online)

Tuesday, March 26 Time 2:00 - 4:00 PM

zoom link: contact Sergei Artemov (sartemov@gmail.com)

Speaker: Thomas Studer, University of Bern

Title: Simplicial Complexes for Epistemic Logic

- - - - Wednesday, Mar 27, 2024 - - - -

- - - - Thursday, Mar 28, 2024 - - - -

- - - - Friday, Mar 29, 2024 - - - -

- - - - Monday, Apr 1, 2024 - - - -

Logic and Metaphysics Workshop

Date: Monday, April 1, 4.15-6.15pm (NY time)

Room: Graduate Center Room 7395

Andrew Tedder (Vienna).

Title: Relevant logics as topical logics

Abstract: There is a simple way of reading a structure of topics into the matrix models of a given logic, namely by taking the topics of a given matrix model to be represented by subalgebras of the algebra reduct of the matrix, and then considering assignments of subalgebras to formulas. The resulting topic-enriched matrix models bear suggestive similarities to the two-component frame models developed by Berto et. al. in Topics of Thought. In this talk I’ll show how this reading of topics can be applied to the relevant logic R, and its algebraic characterisation in terms of De Morgan monoids, and indicate how we can, using this machinery and the fact that R satisfies the variable sharing property, read R as a topic-sensitive logic. I’ll then suggest how this approach to modeling topics can be applied to a broader range of logics/classes of matrices, and gesture at some avenues of research.

- - - - Tuesday, Apr 2, 2024 - - - -

- - - - Wednesday, Apr 3, 2024 - - - -

- - - - Thursday, Apr 4, 2024 - - - -

- - - - Friday, Apr 5, 2024 - - - -

CUNY Graduate Center

Friday, April 5, 12:30pm NY time

Virtual: Please email Victoria Gitman (vgitman@gmail.com) for meeting id.

Kameryn Williams Bard College at Simon's Rock

Logic Workshop

CUNY Graduate Center

Friday April 5, 2:00pm-3:30pm, Room 5417

Decision problem for groups as equivalence relations

In 1911, Dehn proposed three decision problems for finitely presented groups: the word problem, the conjugacy problem, and the isomorphism problem. These problems have been central to both group theory and logic, and were each proven to be undecidable in the 50's. There is much current research studying the decidability of these problems in certain classes of groups.

Classically, when a decision problem is undecidable, its complexity is measured using Turing reducibility. However, Dehn's problems can also be naturally thought of as computably enumerable equivalence relations (ceers). We take this point of view and measure their complexity using computable reductions. This yields behaviors different from the classical context: for instance, every Turing degree contains a word problem, but not every ceer degree does. This leads us to study the structure of ceer degrees containing a word problem and other related questions.

Speakers:

Paul Baginski (Fairfield)

Artem Chernikov (Maryland)

Alf Dolich (CUNY)

Alexei Kolesnikov (Towson)

NEMTD 2024 sponsored by the Mid-Atlantic Mathematical Logic Seminar (NSF grant #DMS-1834219) and the Wesleyan Department of Mathematics and Computer Science.

Organizers: Alex Kruckman, Rehana Patel, Alex Van Abel. Contact akruckman@wesleyan.edu with any questions.

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

(site designed, built & maintained by Victoria Gitman)

## Set theory and topology seminar 26.03.2024 Tomasz Żuchowski

**(Wrocław University of Science and Technology) the lecture:**

**Tomasz Żuchowski**

(on behalf of the organizers, i.e. Piotr Borodulin-Nadzieja, Paweł Krupski, Aleksandra Kwiatkowska, Grzegorz Plebanek, Robert Rałowski and myself)

About 15 minutes before the seminar we invite you for coffee and a chat to social room A.4.1.A in C-19.

https://settheory.pwr.edu.pl/

http://www.math.uni.wroc.pl/seminarium/topologia

## This Week in Logic at CUNY

Rutgers Logic Seminar

Monday Mar 25, 3:30pm, Hill Center, Hill 705

Date: Monday, March 25, 4.15-6.15pm (NY time)

Room: Graduate Center Room 7395

Title: A moderate theory of overall resemblance

Abstract: This paper defends the moderate theory of overall resemblance stated by: A) y is at least as similar to x as z is iff: i) every resemblance property shared by x and z is also shared by x and y, and ii) for any resemblance family of properties F, y is at least as similar to x as z is with respect to F. In this account, a resemblance property is a property that corresponds to a genuine respect in which two things can resemble each other, whereas a resemblance family is a set of properties with respect to which things can be more or less similar to each other. An example of a resemblance property is being cubical, an example of a non-resemblance property is being either a gold cube or a silver sphere, and an example of a resemblance family is the set of specific mass properties.

- - - - Tuesday, Mar 26, 2024 - - - -

Computational Logic Seminar

Spring 2024 (online)

Tuesday, March 26 Time 2:00 - 4:00 PM

zoom link: contact Sergei Artemov (sartemov@gmail.com)

Speaker: Thomas Studer, University of Bern

Title: Simplicial Complexes for Epistemic Logic

- - - - Wednesday, Mar 27, 2024 - - - -

- - - - Thursday, Mar 28, 2024 - - - -

- - - - Friday, Mar 29, 2024 - - - -

- - - - Monday, Apr 1, 2024 - - - -

Logic and Metaphysics Workshop

Date: Monday, April 1, 4.15-6.15pm (NY time)

Room: Graduate Center Room 7395

Andrew Tedder (Vienna).

Title: Relevant logics as topical logics

Abstract: There is a simple way of reading a structure of topics into the matrix models of a given logic, namely by taking the topics of a given matrix model to be represented by subalgebras of the algebra reduct of the matrix, and then considering assignments of subalgebras to formulas. The resulting topic-enriched matrix models bear suggestive similarities to the two-component frame models developed by Berto et. al. in Topics of Thought. In this talk I’ll show how this reading of topics can be applied to the relevant logic R, and its algebraic characterisation in terms of De Morgan monoids, and indicate how we can, using this machinery and the fact that R satisfies the variable sharing property, read R as a topic-sensitive logic. I’ll then suggest how this approach to modeling topics can be applied to a broader range of logics/classes of matrices, and gesture at some avenues of research.

- - - - Tuesday, Apr 2, 2024 - - - -

- - - - Wednesday, Apr 3, 2024 - - - -

- - - - Thursday, Apr 4, 2024 - - - -

- - - - Friday, Apr 5, 2024 - - - -

CUNY Graduate Center

Friday, April 5, 12:30pm NY time

Virtual: Please email Victoria Gitman (vgitman@gmail.com) for meeting id.

Kameryn Williams Bard College at Simon's Rock

Logic Workshop

CUNY Graduate Center

Friday April 5, 2:00pm-3:30pm, Room 5417

Decision problem for groups as equivalence relations

In 1911, Dehn proposed three decision problems for finitely presented groups: the word problem, the conjugacy problem, and the isomorphism problem. These problems have been central to both group theory and logic, and were each proven to be undecidable in the 50's. There is much current research studying the decidability of these problems in certain classes of groups.

Classically, when a decision problem is undecidable, its complexity is measured using Turing reducibility. However, Dehn's problems can also be naturally thought of as computably enumerable equivalence relations (ceers). We take this point of view and measure their complexity using computable reductions. This yields behaviors different from the classical context: for instance, every Turing degree contains a word problem, but not every ceer degree does. This leads us to study the structure of ceer degrees containing a word problem and other related questions.

Speakers:

Paul Baginski (Fairfield)

Artem Chernikov (Maryland)

Alf Dolich (CUNY)

Alexei Kolesnikov (Towson)

NEMTD 2024 sponsored by the Mid-Atlantic Mathematical Logic Seminar (NSF grant #DMS-1834219) and the Wesleyan Department of Mathematics and Computer Science.

Organizers: Alex Kruckman, Rehana Patel, Alex Van Abel. Contact akruckman@wesleyan.edu with any questions.

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

(site designed, built & maintained by Victoria Gitman)

## Wednesday seminar

## 48th Nankai Logic Colloquium

Hello everyone,

This week our weekly Nankai Logic Colloquium is going to be in the afternoon.

This is going to be an online event. Follow the link below to join the Zoom meeting. Please use your real name to join the meeting.

Title ：The 48th Nankai Logic Colloquium -- Dominique LecomteTime ：16:00pm, Mar. 22, 2024(Beijing Time)

Zoom Number ： 734 242 5443

Passcode ：477893

Link ：https://zoom.us/j/7342425443?pwd=NnO2EFts9VOfCR9eDFUkoI3lNn2QTo.1&omn=87996387829

_____________________________________________________________________

The records of past talks can be accessed at https://space.bilibili.com/253421893.

Best wishes,

Ming Xiao

## Logic Seminar 20 March 2024 17:00 hrs by Sun Mengzhou

## This Week in Logic at CUNY

Logic and Metaphysics Workshop

Date: Monday, March 18, 4.15-6.15pm (NY time)

Room: Graduate Center Room 7395

Title: Modal quantifiers, potential infinity, and Yablo sequences

Abstract: 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 omega-inconsistent. Adding either uniform disquotation or the omega-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 omega-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 omega-rule.

Note: This is joint work with Rafał Urbaniak (Gdańsk).

- - - - Tuesday, Mar 19, 2024 - - - -

Roman Kossak, CUNY**The lattice problem for models of PA**

The lattice problem for models of PA is to determine which lattices can be represented either as lattices of elementary substructures of a model of PA or, more generally, which can be represented as lattices of elementary substructures of a model N that contain a given elementary substructure M of N. I will talk about the history of the problem, from the seminal paper of Haim Gaifman from 1976 and other early results to some recent work of Jim Schmerl. There is much to talk about.

**Computational Logic Seminar**

**Spring 2024**

**(online)**

**Tuesday, March 19,**

**Time 2:00 - 4:00 PM**

**Speaker**:

*,*

**Tudor Protopopescu***CUNY*

**Title:**

*Logics of Intuitionistic Knowledge and Verification*

**Abstract:**We present intuitionistic epistemic systems IEL-, IEL and IEL+, systems of verification based belief, knowledge and strict knowledge. The intuitionistic epistemic language captures basic reasoning about intuitionistic knowledge and belief, but its language has expressive limitations. Following Gödel's explication of IPC as a fragment of the more expressive system of classical modal logic S4, we present a faithful embedding of the intuitionistic systems into S4 extended with a verification modality. These systems in turn have explicit counterparts in the Logic of Proofs extended with a verification modality.

The New York City Category Theory Seminar

Department of Computer Science

Department of Mathematics

The Graduate Center of The City University of New York

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

Speaker: ** Sina Hazratpour, Johns Hopkins University.**

Date and Time: ** Wednesday March 20, 2024, 7:00 - 8:30 PM.**

Title:** Fibred Categories in Lean.**

Abstract: Fibred categories are one of the most important and useful concepts in category theory and its application in categorical logic. In this talk I present my recent formalization of fibred categories in the interactive theorem prover Lean 4. I begin by highlighting certain technical challenges associated with handling the equality of objects and functors within the extensional dependent type system of Lean, and how they can be overcome. In this direction, I will demonstrate how we can take advantage of dependent coercion, instance synthesis, and automation tactics from the Lean toolbox. Finally I will discuss a formalization of Homotopy Type Theory in Lean 4 using a fired categorical framework.

- - - - Thursday, Mar 21, 2024 - - - -

- - - - Friday, Mar 22, 2024 - - - -

CUNY Graduate Center

Friday, March 22, 12:30pm NY time

Virtual: Please email Victoria Gitman (vgitman@gmail.com) for meeting id.

**Arthur Apter**, CUNY**A choiceless answer to a question of Woodin**

In a lecture presented in July 2023, Moti Gitik discussed the following question from the 1980s due to Woodin, as well as approaches to its solution and why it is so difficult to solve:

Question: Assuming there is no inner model of ZFC with a strong cardinal, is it possible to have a model of ZFC such that ' and for every ', together with the existence of an inner model of ZFC such that for the so that and ' is measurable and '?I will discuss how to find answers to this question, if we drop the requirement that satisfies the Axiom of Choice. I will also briefly discuss the phenomenon that on occasion, when the Axiom of Choice is removed from consideration, a technically challenging question or problem becomes more tractable. One may, however, end up with models satisfying conclusions that are impossible in ZFC.

Reference: A. Apter, 'A Note on a Question of Woodin', *Bulletin of the Polish Academy of Sciences (Mathematics)*, volume 71(2), 2023, 115--121.

CUNY Graduate Center

**Mediate cardinals**

In the late 1910s Bertrand Russell was occupied with two things: getting into political trouble for his pacifism and trying to understand the foundations of mathematics. His students were hard at work with him on this second occupation. One of those students was Dorothy Wrinch. In 1923 she gave a characterization of the axiom of choice in terms of a generalization of the notion of a Dedekind-finite infinite set. Unfortunately, her career turned toward mathematical biology and her logical work was forgotten by history.

This talk is part of a project of revisiting Wrinch's work from a modern perspective. I will present the main result of her 1923 paper, that AC is equivalent to the non-existence of what she termed mediate cardinals. I will also talk about some new independence results. The two main results are: (1) the smallest for which a -mediate cardinal exists can consistently be any regular and (2) the collection of regular for which exact -mediate cardinals exist can consistently be any class.

- - - - Monday, Mar 25, 2024 - - - -

Logic and Metaphysics Workshop

Date: Monday, March 25, 4.15-6.15pm (NY time)

Room: Graduate Center Room 7395

Title: A moderate theory of overall resemblance

Abstract: This paper defends the moderate theory of overall resemblance stated by: A) y is at least as similar to x as z is iff: i) every resemblance property shared by x and z is also shared by x and y, and ii) for any resemblance family of properties F, y is at least as similar to x as z is with respect to F. In this account, a resemblance property is a property that corresponds to a genuine respect in which two things can resemble each other, whereas a resemblance family is a set of properties with respect to which things can be more or less similar to each other. An example of a resemblance property is being cubical, an example of a non-resemblance property is being either a gold cube or a silver sphere, and an example of a resemblance family is the set of specific mass properties.

- - - - Tuesday, Mar 26, 2024 - - - -

- - - - Wednesday, Mar 27, 2024 - - - -

- - - - Thursday, Mar 28, 2024 - - - -

- - - - Friday, Mar 29, 2024 - - - -

WHERE: Rutgers, The State University of New Jersey.

WHEN: Saturday, March 23

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

(site designed, built & maintained by Victoria Gitman)

## KGRC Talk - March 21

## Set theory and topology seminar 19.03.2024 Piotr Szewczak

**(Wrocław University of Science and Technology) the lecture:**

**Piotr Szewczak (UKSW)**

*perfectly meager in the transitive sense*if for any perfect set P there is an F-sigma set F containing X such that for every point t the intersection of t+F and P is meager in the relative topology of P. A set X is

*Hurewicz*if for any sequence of increasing open covers of X one can select one set from each cover such that the chosen sets formulate a gamma-cover of X, i.e., an infinite cover such that each point from X belongs to all but finitely many sets from the cover. Nowik proved that each Hurewicz set which cannot be mapped continuously onto the Cantor set is perfectly meager in the transitive sense. We answer a question of Nowik and Tsaban, whether of the same assertion holds for each Hurewicz set with no copy of the Cantor set inside. We solve this problem, under CH, in the negative.

(on behalf of the organizers, i.e. Piotr Borodulin-Nadzieja, Paweł Krupski, Aleksandra Kwiatkowska, Grzegorz Plebanek, Robert Rałowski and myself)

About 15 minutes before the seminar we invite you for coffee and a chat to social room A.4.1.A in C-19.

https://settheory.pwr.edu.pl/

http://www.math.uni.wroc.pl/seminarium/topologia

## Wednesday seminar

## 47th Nankai Logic Colloquium

Hello everyone,

This week our weekly Nankai Logic Colloquium is going to be in the morning.

Our speaker this week will be Sumun Iyer from Cornell University. This talk is going to take place this Friday, Mar 15, from 9am to 10am(UTC+8, Beijing time).

This is going to be an online event. Follow the link below to join the Zoom meeting. Please use your real name to join the meeting.

Title ：The 47th Nankai Logic Colloquium -- Sumun Iyer

Time ：9:00am, Mar. 15, 2024(Beijing Time)

Zoom Number ： 734 242 5443

Passcode ：477893

Link ：https://zoom.us/j/7342425443?pwd=EG6I3uatr8anqkk6HM5wZ9FKjhkjbC.1&omn=87197636384

_____________________________________________________________________

Best wishes,

Ming Xiao

## This Week in Logic at CUNY

Logic and Metaphysics Workshop

Date: Monday, March 11, 4.15-6.15pm (NY time)

Room: Graduate Center Room 7395

Title: Dispensing with the grounds of logical necessity

Abstract: Logical laws are typically conceived as being necessary. But in virtue of what is this the case? That is, what are the grounds of logical necessity? In this paper, I examine four different answers to this question in terms of: truth-conditions, invariance of truth-values under different interpretations, possible worlds, and brute facts. I ultimately find all of them wanting. I conclude that an alternative conception of logic that dispenses altogether with grounds of logical necessity provides a less troublesome alternative. I then indicate some of the central features of this conception.

- - - - Tuesday, Mar 12, 2024 - - - -

Albert Visser, Utrecht University**Restricted completions**

This talk reports on research in collaboration with Ali Enayat and Mateusz Łełyk.

Steffen Lempp and Dino Rossegger asked: is there a consistent completion of that is axiomatised by sentences of bounded quantifier-alternation complexity? We show that there is no such restricted completion. We also show that, if one changes the measure of complexity to being , there is a restricted completion. Specifically, we show that the true theory of the non-negative part of can be axiomatised by a single sentence plus a set of -sentences.In our talk we will sketch these two answers. One of our aims is to make clear is that the negative answer for the case of quantifier-alternation complexity simply follows from Rosser's Theorem viewed from a sufficiently abstract standpoint.

- - - - Wednesday, Mar 13, 2024 - - - -

- - - - Thursday, Mar 14, 2024 - - - -

- - - - Friday, Mar 15, 2024 - - - -

CUNY Graduate Center

Friday, March 15, 12:30pm NY time

Virtual: Please email Victoria Gitman (vgitman@gmail.com) for meeting id.

**Squares, ultrafilters and forcing axioms**

A uniform ultrafilter over a cardinal is called *indecomposable* if, whenever and , there is a set such that is countable. Indecomposability is a natural weakening of -completeness and has a number of implications for, e.g., the structure of ultraproducts. In the 1980s, Sheard answered a question of Silver by proving the consistency of the existence of an inaccessible but not weakly compact cardinal carrying an indecomposable ultrafilter. Recently, however, Goldberg proved that this situation cannot hold above a strongly compact cardinal: If is strongly compact and carries an indecomposable ultrafilter, then is either measurable or a singular limit of countably many measurable cardinals. We prove that the same conclusion follows from the Proper Forcing Axiom, thus adding to the long list of statements first shown to hold above a strongly compact or supercompact cardinal and later shown also to follow from PFA. Time permitting, we will employ certain indexed square principles to prove that our results are sharp. This is joint work with Assaf Rinot and Jing Zhang.

CUNY Graduate Center

**Tennebaum's Theorem for quotient presentations and model-theoretic skepticism**

A computable quotient presentation of a mathematical structure consists of a computable structure on the natural numbers , meaning that the operations and relations of the structure are computable, and an equivalence relation on , not necessarily computable but which is a congruence with respect to this structure, such that the quotient is isomorphic to the given structure . Thus, one may consider computable quotient presentations of graphs, groups, orders, rings and so on.

A natural question asked by B. Khoussainov in 2016, is if the Tennenbaum Thoerem extends to the context of computable presentations of nonstandard models of arithmetic. In a joint work with J.D. Hamkins we have proved that no nonstandard model of arithmetic admits a computable quotient presentation by a computably enumerable equivalence relation on the natural numbers.

However, as it happens, there exists a nonstandard model of arithmetic admitting a computable quotient presentation by a co-c.e. equivalence relation. Actually, there are infinitely many of those. The idea of the proof consists is simulating the Henkin construction via finite injury priority argument. What is quite surprising, the construction works (i.e. injury lemma holds) by Hilbert's Basis Theorem. The latter argument is joint work with T. Slaman and L. Harrington.

- - - - Monday, Mar 18, 2024 - - - -

Logic and Metaphysics Workshop

Date: Monday, March 18, 4.15-6.15pm (NY time)

Room: Graduate Center Room 7395

Title: Modal quantifiers, potential infinity, and Yablo sequences

Abstract: 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 omega-inconsistent. Adding either uniform disquotation or the omega-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 omega-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 omega-rule.

Note: This is joint work with Rafał Urbaniak (Gdańsk).

- - - - Tuesday, Mar 19, 2024 - - - -

- - - - Wednesday, Mar 20, 2024 - - - -

The New York City Category Theory Seminar

Department of Computer Science

Department of Mathematics

The Graduate Center of The City University of New York

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

Speaker: ** Sina Hazratpour, Johns Hopkins University.**

Date and Time: ** Wednesday March 20, 2024, 7:00 - 8:30 PM.**

Title:** Fibred Categories in Lean.**

Abstract: Fibred categories are one of the most important and useful concepts in category theory and its application in categorical logic. In this talk I present my recent formalization of fibred categories in the interactive theorem prover Lean 4. I begin by highlighting certain technical challenges associated with handling the equality of objects and functors within the extensional dependent type system of Lean, and how they can be overcome. In this direction, I will demonstrate how we can take advantage of dependent coercion, instance synthesis, and automation tactics from the Lean toolbox. Finally I will discuss a formalization of Homotopy Type Theory in Lean 4 using a fired categorical framework.

- - - - Thursday, Mar 21, 2024 - - - -

- - - - Friday, Mar 22, 2024 - - - -

CUNY Graduate Center

Friday, March 22, 12:30pm NY time

Virtual: Please email Victoria Gitman (vgitman@gmail.com) for meeting id.

**Arthur Apter**, CUNY**A choiceless answer to a question of Woodin**

In a lecture presented in July 2023, Moti Gitik discussed the following question from the 1980s due to Woodin, as well as approaches to its solution and why it is so difficult to solve:

Question: Assuming there is no inner model of ZFC with a strong cardinal, is it possible to have a model of ZFC such that ' and for every ', together with the existence of an inner model of ZFC such that for the so that and ' is measurable and '?I will discuss how to find answers to this question, if we drop the requirement that satisfies the Axiom of Choice. I will also briefly discuss the phenomenon that on occasion, when the Axiom of Choice is removed from consideration, a technically challenging question or problem becomes more tractable. One may, however, end up with models satisfying conclusions that are impossible in ZFC.

Reference: A. Apter, 'A Note on a Question of Woodin', *Bulletin of the Polish Academy of Sciences (Mathematics)*, volume 71(2), 2023, 115--121.

CUNY Graduate Center

WHERE: Rutgers, The State University of New Jersey.

WHEN: Saturday, March 23

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@citytech.cuny.edu.

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

## KGRC Talks - March 11-15

## Set theory and topology seminar 12.03.2024 Grigor Sargsyan

**(Wrocław University of Science and Technology) the lecture:**

**Grigor Sargsyan (IMPAN)**

https://settheory.pwr.edu.pl/

http://www.math.uni.wroc.pl/seminarium/topologia

## Wednesday seminar

## KGRC Set Theory Talks - March 4-8

Alexi Block Gorman, Ohio State University, Columbus, US (host: Matthias Aschenbrenner) visits March 3–9

Elliot Kaplan, McMaster University, Hamilton, CA, Columbus, US (host: Nigel Pynn-Coates) visits March 3–9

Silvan Horvath, ETH Zurich, CH (host: Vera Fischer) visits March 4–July 31

* * * * * * * * *

KGRC/Institute of Mathematics invites you to the following talks:

(updates at https://kgrc.univie.ac.at/) )

**SET THEORY SEMINAR**

Kolingasse 14–16, 1090, 1st floor, SR 10,

Thursday, March 7, 11:30am – 12:00pm, hybrid mode

**”Magic Sets”**

S. Horvath (ETH Zurich, CH)

S. Horvath (ETH Zurich, CH)

A Magic Set is a set M of reals with the property that for all nowhere constant, continuous functions f and

g on the reals it holds that f [M ] ⊆ g[M ] implies f = g.

I will cover some of the basic results on magic sets and introduce magic forcing - a forcing notion that adds

a new magic set to the ground model.

Zoom: If you have not received the Zoom data by the day before the talk, please contact petra.czarnecki@univie.ac.at.

Meeting ID: 671 1734 6051

Passcode: kgrc

Please direct any questions about this talk to vera.fischer@univie.ac.at.

* * * * * * * * *

**SET THEORY SEMINAR**

Kolingasse 14–16, 1090, 1st floor, SR 10,

Thursday, March 7, 12:00pm – 13:00pm, hybrid mode

**”A general theory of iterated forcing using finitely additive measures”**

A. F. Uribe Zapata (TU Wien)

A. F. Uribe Zapata (TU Wien)

Saharon Shelah in 2000 introduced a finite-support iteration using finitely additive measures to prove that,

consistently, the covering of the null ideal may have countable cofinality. In 2019, Jakob Kellner, Saharon

Shelah, and Anda R. T ̆anasie achieved some new results and applications using such iterations.

In this talk, based on the works mentioned above, we present a general theory of iterated forcing using

finitely additive measures, which was developed in the speaker’s master’s thesis. For this purpose, we intro-

duce two new notions: on the one hand, we define a new linkedness property, which we call ”FAM-linked”

and, on the other hand, we generalize the idea of intersection number to forcing notions, which justifies the

limit steps of our iteration theory. Finally, we show a new separation of the left-side of Cicho ́n’s diagram

allowing a singular value.

Zoom info

Zoom: If you have not received the Zoom data by the day before the talk, please contact petra.czarnecki@univie.ac.at.

Passcode: kgrc

Please direct any questions about this talk to vera.fischer@univie.ac.at.

* * * * * * * * *

**VIDEO**recordings available so far of the

**LOGIC COLLOQUIUM:**

January 25: Y. Khomskii (Amsterdam U College, NL and U Hamburg, DE) "Trees, Transcendence and Quasi-generic reals"https://ucloud.univie.ac.at/index.php/s/Wd9DPzXqQsnBPzC

November 16: D. A. Mejía (Shizuoka U, JP) ”Iterations with ultrafilter-limits and fam-limits” https://ucloud.univie.ac.at/index.php/s/T6pD2XgwTfNPYtn

—–

The LECTURE NOTE for Diego Mejía’s mini-course available so far of the Set Theory Seminar:

January 25: D. A. Mejıa (Shizuoka U, JP) ”Forcing techniques for Cicho ́n’s Maximum” https://mathematik.univie.ac.at/fileadmin/user_upload/f_mathematik/Events_News/Vortraege_Events/2023-24/20240122_Mejia_minicourse-1.pdf.

**VIDEO**recordings available so far of the

**SET THEORY SEMINAR**:

January 25: D. A. Mejía (Shizuoka U, JP), ”Forcing techniques for Cicho ́n’s Maximum VI” video: https://ucloud.univie.ac.at/index.php/s/8EyKfLZW3NBH4f2

January 18: D. A. Mejía (Shizuoka U, JP), ”Forcing techniques for Cicho ́n’s Maximum V” video:https://ucloud.univie.ac.at/index.php/s/QrKjY6CYtJMx7WT

January 11: D. A. Mejía (Shizuoka U, JP), ”Forcing techniques for Cicho ́n’s Maximum IV” https://ucloud.univie.ac.at/index.php/s/KFpbqsLjQm3tcKn

December 7: "Forcing techniques for Cichoń's Maximum: FS iterations II" video:https://ucloud.univie.ac.at/index.php/s/iwqKFiYCEpPaPsN

November 30: "Forcing techniques for Cichoń's Maximum I" video: https://ucloud.univie.ac.at/index.php/s/xWjSe9eA92ReRV9

-- Mag. Petra Czarnecki de Czarnce-Chalupa Institute of Mathematics (Kurt Goedel Research Center, Logic) University of Vienna Kolingasse 14-16, #7.48 1090 Vienna, Austria Phone: +43/ (0)1 4277-50501

## NUS Logic Seminar Talk by Rupert Hoelzl on 6 March 2024 17:00 hrs

## Set theory and topology seminar 5.03.2024 Agnieszka Widz

**(Wrocław University of Science and Technology) the lecture:**

**Agnieszka Widz**

https://settheory.pwr.edu.pl/

http://www.math.uni.wroc.pl/seminarium/topologia

## This Week in Logic at CUNY

Rutgers Logic Seminar

Monday, March 4, 3:30pm, Rutgers University, Hill 705

Logic and Metaphysics Workshop

Date: Monday, March 4, 4.15-6.15pm (NY time)

Room: Graduate Center Room 7395

Elise Crull (CUNY).

Title: Declaring no dependence

Abstract: Viable fundamental ontologies require at least one suitably stable, generic-yet-toothy metaphysical dependence relation to establish fundamentality. In this talk I argue that recent experiments in quantum physics using Page-Wootters devices to model global vs. local dynamics cast serious doubt on the existence of such metaphysical dependence relations when – and arguably, inevitably within any ontological framework – physical systems serve as the relata.

- - - - Tuesday, Mar 5, 2024 - - - -

**Tightness and solidity in fragments of Peano Arithmetic**

It was shown by Visser that Peano Arithmetic has the property that no two distinct extensions of it (in its language) are bi-interpretable. Enayat proposed to refer to this property of a theory as *tightness* and to carry out a more systematic study of tightness and its stronger variants, which he called *neatness* and *solidity*.

Enayat proved that not only , but also , , and are solid; and on the other hand, that finitely axiomatisable fragments of them are not even tight. Later work by a number of authors showed that many natural proper fragments of these theories are also not tight.

Enayat asked whether there are proper solid subtheories (containing some basic axioms that depend on the theory) of the theories listed above. We answer this question in the case of by proving that for every there exists a solid theory strictly between and . Furthermore, we can require that the theory does not interpret , and that if any true arithmetic sentence is added to it, the theory still does not prove .

Joint work with Leszek Kołodziejczyk and Mateusz Łełyk.

Spring 2024 (online) For a zoom link contact S.Artemov

Tuesday, March 5, Time 2:00 - 4:00 PM

Speaker: Sergei Artemov, Graduate Center

Title: On Tolerance Analysis in Extensive-Form Games.

- - - - Wednesday, Mar 6, 2024 - - - -

The New York City Category Theory Seminar

Department of Computer Science

Department of Mathematics

The Graduate Center of The City University of New York

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

Speaker: ** Jean-Pierre Marquis, Universite de Montreal.**

Date and Time: ** Wednesday March 6, 2024, 7:00 - 8:30 PM. IN PERSON TALK!**

Title:** Hom sweet Hom: a sketch of the history of duality in category theory.**

Abstract: Duality, in its various forms and roles, played a surprisingly important part in the development of category theory. In this talk, I will concentrate on the development of these forms and roles that lead to the categorical formulation of Stone-type dualities in the 1970s. I will emphasize the epistemological gain and loss along the way.

- - - - Thursday, Mar 7, 2024 - - - -

- - - - Friday, Mar 8, 2024 - - - -

CUNY Graduate Center

Friday, March 8, 12:30pm NY time

Virtual: Please email Victoria Gitman (vgitman@gmail.com) for meeting id.

- - - - Monday, Mar 11, 2024 - - - -

Logic and Metaphysics Workshop

Date: Monday, March 11, 4.15-6.15pm (NY time)

Room: Graduate Center Room 7395

Title: Dispensing with the grounds of logical necessity

Abstract: Logical laws are typically conceived as being necessary. But in virtue of what is this the case? That is, what are the grounds of logical necessity? In this paper, I examine four different answers to this question in terms of: truth-conditions, invariance of truth-values under different interpretations, possible worlds, and brute facts. I ultimately find all of them wanting. I conclude that an alternative conception of logic that dispenses altogether with grounds of logical necessity provides a less troublesome alternative. I then indicate some of the central features of this conception.

- - - - Tuesday, Mar 12, 2024 - - - -

Albert Visser, Utrecht University**Restricted completions**

This talk reports on research in collaboration with Ali Enayat and Mateusz Łełyk.

Steffen Lempp and Dino Rossegger asked: is there a consistent completion of that is axiomatised by sentences of bounded quantifier-alternation complexity? We show that there is no such restricted completion. We also show that, if one changes the measure of complexity to being , there is a restricted completion. Specifically, we show that the true theory of the non-negative part of can be axiomatised by a single sentence plus a set of -sentences.In our talk we will sketch these two answers. One of our aims is to make clear is that the negative answer for the case of quantifier-alternation complexity simply follows from Rosser's Theorem viewed from a sufficiently abstract standpoint.

- - - - Wednesday, Mar 13, 2024 - - - -

- - - - Thursday, Mar 14, 2024 - - - -

- - - - Friday, Mar 15, 2024 - - - -

CUNY Graduate Center

Friday, March 15, 12:30pm NY time

Virtual: Please email Victoria Gitman (vgitman@gmail.com) for meeting id.

CUNY Graduate Center

WHERE: Rutgers, The State University of New Jersey.

WHEN: Saturday, March 23

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@citytech.cuny.edu.

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

## Wednesday seminar

## Wednesday seminar

## 45th Nankai Logic Colloquium

Hello everyone,

Our speaker this week will be Takayuki Kihara from Nagoya University. This talk is going to take place this Friday, Mar. 01, from 4pm to 5pm(UTC+8, Beijing time).

```
[Title]
On the Wadge degrees of Borel partitions
[Abstract]
In descriptive set theory, there are a lot of semi-well-ordered hierarchies, such as the Borel hierarchy, the projective hierarchy, and the difference hierarchy. Under AD, their ultimate refinement is provided by the Wadge degrees, which is also semi-well-ordered.
Now, the question arises: what exactly gives rise to this semi-well-ordered structure?
Our goal is to reveal the true structure behind this semi-well-order. To achieve this, it is crucial to handle not subsets (two-valued functions) but partitions (k-valued functions). As long as we only observe two-valued functions, all dynamic mechanisms lurking behind collapse, appearing to our eyes only as a semi-well-order. By dealing with partitions, we can expose the ultimate dynamic structure that was concealed. What existed there is not a semi-well-order but rather a better quasi-order, -- a sort of transfinite "matryoshkas" of trees.
```

The records of past talks can be accessed at https://space.bilibili.com/253421893.

Best Wishes,

Ming Xiao

## Cross-Alps Logic Seminar (speaker: Simon Henry)

**Simon Henry**(University of Ottawa)

*Higher categorical language*## This Week in Logic at CUNY

Logic and Metaphysics Workshop

Date: Monday, Feb 26, 4.15-6.15pm (NY time)

Room: Graduate Center Room 7395

Matteo Plebani (Turin).

Title: Semantic paradoxes as collective tragedies

Abstract: What does it mean to solve a paradox? A common assumption is that to solve a paradox we need to find the wrong step in a certain piece of reasoning. In this talk, I will argue while in the case of some paradoxes such an assumption might be correct, in the case of paradoxes such as the liar and Curry’s paradox it can be questioned.

- - - - Tuesday, Feb 27, 2024 - - - -

Computational Logic Seminar

Spring 2024 (online)

Tuesday, February 27, 2:00 - 4:00 PM

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

Speaker: Vincent Peluce, Graduate Center

Title: What is Intuitionistic Arithmetic

- - - - Wednesday, Feb 28, 2024 - - - -

The New York City Category Theory Seminar

Department of Computer Science

Department of Mathematics

The Graduate Center of The City University of New York

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

**Astra Kolomatskaia, Stony Brook.**

**Wednesday February 28, 2024, 7:00 - 8:30 PM. IN PERSON TALK!**

**Room 6417**

**Displayed Type Theory and Semi-Simplicial Types.**

- - - - Thursday, Feb 29, 2024 - - - -

- - - - Friday, Mar 1, 2024 - - - -

CUNY Graduate Center

Rehana Patel Wesleyan University

CUNY Graduate Center

Alf Dolich, CUNY**Component Closed Structures on the Reals**

A structure, R, expanding is called component closed if whenever is definable so are all of 's connected components. Two basic examples of component closed structures are and . It turns out that these two structures are exemplary of a general phenomenon for component closed structures from a broad class of expansions of : either their definable sets are very 'tame' (as in the case of the real closed field) or they are quite 'wild' (as in the case of the real field expanded by the integers).

- - - - Monday, Mar 4, 2024 - - - -

Rutgers Logic Seminar

Monday, March 4, 3:30pm, Rutgers University, Hill 705

Logic and Metaphysics Workshop

Date: Monday, March 4, 4.15-6.15pm (NY time)

Room: Graduate Center Room 7395

Elise Crull (CUNY).

Title: Declaring no dependence

Abstract: Viable fundamental ontologies require at least one suitably stable, generic-yet-toothy metaphysical dependence relation to establish fundamentality. In this talk I argue that recent experiments in quantum physics using Page-Wootters devices to model global vs. local dynamics cast serious doubt on the existence of such metaphysical dependence relations when – and arguably, inevitably within any ontological framework – physical systems serve as the relata.

- - - - Tuesday, Mar 5, 2024 - - - -

- - - - Wednesday, Mar 6, 2024 - - - -

The New York City Category Theory Seminar

Department of Computer Science

Department of Mathematics

The Graduate Center of The City University of New York

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

Speaker: ** Jean-Pierre Marquis, Universite de Montreal.**

Date and Time: ** Wednesday March 6, 2024, 7:00 - 8:30 PM. IN PERSON TALK!**

Title:** Hom sweet Hom: a sketch of the history of duality in category theory.**

Abstract: Duality, in its various forms and roles, played a surprisingly important part in the development of category theory. In this talk, I will concentrate on the development of these forms and roles that lead to the categorical formulation of Stone-type dualities in the 1970s. I will emphasize the epistemological gain and loss along the way.

- - - - Thursday, Mar 7, 2024 - - - -

- - - - Friday, Mar 8, 2024 - - - -

CUNY Graduate Center

Friday, March 8, 12:30pm NY time

Virtual: Please email Victoria Gitman (vgitman@gmail.com) for meeting id.

WHERE: Rutgers, The State University of New Jersey.

WHEN: Saturday, March 23

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@citytech.cuny.edu.

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## Wednesday seminar

## 44th Nankai Logic Colloquium

Hello everyone,

Our speaker this week will be Clark Lyons from the University of California, Los Angeles. This talk is going to take place this Friday, Feb 23, from 9am to 10am(UTC+8, Beijing time).

Title: Baire Measurable Matchings in Non-amenable Graphs Abstract: Tutte's theorem provides a necessary and sufficient condition for a finite graph to have a perfect matching. In this talk I will present joint work with Kastner showing that if a locally finite Borel graph satisfies a strengthened form of Tutte's condition, then it has a perfect matching which is Baire measurable. As a consequence, the Schreier graph of a free action of a non-amenable group on a Polish space admits a Baire measurable perfect matching. This is analogous to the result of Csoka and Lippner on factor of IID perfect matchings for non-amenable Cayley graphs.

The records of past talks can be accessed at https://space.bilibili.com/253421893.

Best Wishes,

Ming Xiao

## Set theory and topology seminar 27.02.2024 Grzegorz Plebanek

**(Wrocław University of Science and Technology) the lecture:**

**Grzegorz Plebanek**

https://settheory.pwr.edu.pl/

http://www.math.uni.wroc.pl/seminarium/topologia

## Wednesday seminar

## This Week in Logic at CUNY

Rutgers Logic Seminar

Monday, Feb 19, 3:30pm, Rutgers University, Hill 705

Artem Chernikov, Maryland

Intersecting sets in probability spaces and Shelah's classification

- - - - Tuesday, Feb 20, 2024 - - - -

**Computational Logic Seminar**

**Spring 2024**

**(online)**

**Tuesday, February 20**

**Time 2:00 - 4:00 PM**

**Speaker**:

**,**

*Matteo Plebani**The University of Turin*

**Title:**

*Counterpossibles in relative computability theory: a closer look*

**Abstract:**A counterpossible is a counterfactual with an impossible antecedent, like “if zero were equal to one, two would be equal to five”. Matthias Jenny [Jenny, 2018] has argued that the following is an example of a false counterpossible:

HT If the validity problem were algorithmically solvable, then arithmetical truth would be also algorithmically decidable

As Jenny himself emphasizes, establishing that HT is a false counterpossible would be highly significant. According to the standard analysis of counterfactuals ([Lewis, 1973], [Stalnaker, 1968]) all counterpossibles are vacuously true. If HT is false, then, the standard analysis of counterfactuals is wrong.

In this paper, we will argue that HT admits two readings, which are expressed by two different ways of formalizing HT. Under the first reading, HT is clearly a counterpossible. Under the second reading, HT is clearly false. Hence, it is possible to read HT as a counterpossible (section 2) and it is possible to read HT as a false claim (section 3). However, it is unclear that it is possible to do both things at once, i.e. interpret HT as a false counterpossible.

It can be proven that the two readings are not equivalent. The formalization expressing the first reading is a mathematical theorem, which means that under the first reading, HT is a true counterpossible. On the other hand, I will argue that under the second reading HT, while false, is best interpreted as a counterpossible with a contingent antecedent.

- - - - Wednesday, Feb 21, 2024 - - - -

- - - - Thursday, Feb 22, 2024 - - - -

- - - - Friday, Feb 23, 2024 - - - -

CUNY Graduate Center

**Commutativity of cofinal types of ultrafilters**

- - - - Monday, Feb 26, 2024 - - - -

Logic and Metaphysics Workshop

Date: Monday, Feb 26, 4.15-6.15pm (NY time)

Room: Graduate Center Room 7395

Matteo Plebani (Turin).

Title: Semantic paradoxes as collective tragedies

Abstract: What does it mean to solve a paradox? A common assumption is that to solve a paradox we need to find the wrong step in a certain piece of reasoning. In this talk, I will argue while in the case of some paradoxes such an assumption might be correct, in the case of paradoxes such as the liar and Curry’s paradox it can be questioned.

- - - - Tuesday, Feb 27, 2024 - - - -

- - - - Wednesday, Feb 28, 2024 - - - -

The New York City Category Theory Seminar

Department of Computer Science

Department of Mathematics

The Graduate Center of The City University of New York

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

**Astra Kolomatskaia, Stony Brook.**

**Wednesday February 28, 2024, 7:00 - 8:30 PM. IN PERSON TALK!**

**Room 6417**

**Displayed Type Theory and Semi-Simplicial Types.**

In this talk, we will construct semi-simplicial types in Displayed Type Theory [dTT], a fully semantically general homotopy type theory. Many of our main results are independent of type theory and will say something new and surprising about the homotopy theoretic notion of a classifier for semi-simplicial objects.

This talk is based on joint work with Michael Shulman. Reference: https://arxiv.org/abs/2311.18781

- - - - Thursday, Feb 29, 2024 - - - -

- - - - Friday, Mar 1, 2024 - - - -

CUNY Graduate Center

Rehana Patel Wesleyan University

CUNY Graduate Center

Alf Dolich, CUNY**Component Closed Structures on the Reals**

A structure, R, expanding is called component closed if whenever is definable so are all of 's connected components. Two basic examples of component closed structures are and . It turns out that these two structures are exemplary of a general phenomenon for component closed structures from a broad class of expansions of : either their definable sets are very 'tame' (as in the case of the real closed field) or they are quite 'wild' (as in the case of the real field expanded by the integers).

WHERE: Rutgers, The State University of New Jersey.

WHEN: Saturday, March 23

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

(site designed, built & maintained by Victoria Gitman)

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

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## Logic Seminar Wed 21.02.2024 17:00 hrs at NUS by Neil Barton

## This Week in Logic at CUNY

Rutgers Logic Seminar

Monday, Feb 12, 3:30pm, Rutgers University, Hill 705

For a cardinal $\kappa\ge 2$, one can weaken the classical concept "x is ordinal definable" (i.e., x is the unique object satisfying some condition involving ordinal parameters) to "x is <$\kappa$-blurrily ordinal definable," meaning that x is one of fewer than $\kappa$ many objects satisfying some condition involving ordinal parameters. By considering the hereditary version of this, one naturally arrives at the inner model <$\kappa$-HOD, the class of all hereditarily <$\kappa$-blurrily ordinal definable sets. In ZFC, by varying $\kappa$, one obtains a hierarchy of inner models spanning the entire spectrum from HOD to V. Those stages in the hierarchy where something new is added I call leaps.

I will give an overview of what is known about this hierarchy: ZFC-provable facts regarding the relationships between the stages of the hierarchy and the basic structure of leaps, and consistency results on leap constellations, including consistency strength determinations.

- - - - Tuesday, Feb 13, 2024 - - - -

MOPA

The Borel hierarchy gives a robust way to stratify the complexity of sets of countable structures and is intimately tied with definability in infinitary logic via the Lopez-Escobar theorem. However, what happens with sets axiomatizable in finitary first-order logic, such as the set of structures satisfying a given finitary first-order theory T? Is the complexity of the set of T's models in any way related to the quantifier complexity of the sentences axiomatizing it? In particular, if a theory T is not axiomatizable by a set of sentences of bounded quantifier complexity, can the set of models of T still be at a finite level of the Borel hierarchy?

In this talk, we will present results concerning these questions:

In joint work with Andrews, Gonzalez, Lempp, and Zhu we show that the set of models of a theory T is -complete if and only if T does not have an axiomatization by sentences of bounded quantifier complexity, answering the last question in the negative. We also characterize the Borel complexity of the set of models of complete theories in terms of their finitary axiomatizations. Our results suggest that infinitary logic does not provide any efficacy when defining first-order properties, a phenomenon already observed by Wadge and Keisler and, recently, rediscovered by Harrison-Trainor and Kretschmer using different techniques.

Combining our results with recent results by Enayat and Visser, we obtain that a large class of theories studied in the foundations of mathematics, sequential theories, have a maximal complicated set of models.

**Computational Logic Seminar**

**Spring 2024**

**(online)**

**Tuesday, February 13**

**Speaker**: Melvin Fitting, CUNY Graduate Center

**Title:**

*About Semantic Tableaus*

**Abstract:**I will sketch the basics of tableau proof systems, beginning with those for classical propositional logic. Then I will move to intuitionistic tableaus and modal tableaus (more than one kind of tableau system). Finally I’ll say something about quantifiers. Slides exist for the beginning part of the talk. When they run out I’ll work on the Zoom equivalent of a blackboard.

- - - - Wednesday, Feb 14, 2024 - - - -

- - - - Thursday, Feb 15, 2024 - - - -

- - - - Friday, Feb 16, 2024 - - - -

**Largeness notions**

Finite Ramsey Theorem states that fixed , there exists such that for each coloring of with colors, there is a homogeneous subset of of cardinality at least . Starting with the celebrated Paris-Harrington theorem, many Ramsey-like results have been studied using different largeness notions rather than the cardinality. I will introduce the largeness notion defined by Ketonen and Solovay based on fundamental sequences of ordinals. Then I will describe an alternative and more flexible largeness notion using blocks and barriers. If time allows, I will talk about how the latter can be used to study a more general Ramsey-like result.

CUNY Graduate Center

**The Ginsburg-Sands theorem and computability**

In their 1979 paper `Minimal Infinite Topological Spaces,’ Ginsburg and Sands proved that every infinite topological space has an infinite subspace homeomorphic to exactly one of the following five topologies on : indiscrete, discrete, initial segment, final segment, and cofinite. The proof, while nonconstructive, features an interesting application of Ramsey's theorem for pairs (). We analyze this principle in computability theory and reverse mathematics, using Dorais's formalization of CSC spaces. Among our results are that the Ginsburg-Sands theorem for CSC spaces is equivalent to while for Hausdorff spaces it is provable in . Furthermore, if we enrich a CSC space by adding the closure operator on points, then the Ginsburg-Sands theorem turns out to be equivalent to the Chain-Antichain Principle (). The most surprising case is that of the Ginsburg-Sands theorem restricted to spaces. Here, we show that the principle lies strictly between and , yielding perhaps the first natural theorem of ordinary mathematics (i.e., conceived outside of logic) to occupy this interval. I will discuss the proofs of both the implications and separations, which feature several novel combinatorial elements, and survey a new class of purely combinatorial principles below and not implied by revealed by our investigation. This is joint work with Heidi Benham, Andrew DeLapo, Reed Solomon, and Java Darleen Villano.

- - - - Monday, Feb 19, 2024 - - - -

- - - - Tuesday, Feb 20, 2024 - - - -

- - - - Wednesday, Feb 21, 2024 - - - -

- - - - Thursday, Feb 22, 2024 - - - -

- - - - Friday, Feb 23, 2024 - - - -

CUNY Graduate Center

WHERE: Rutgers, The State University of New Jersey.

WHEN: Saturday, March 23

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

(site designed, built & maintained by Victoria Gitman)

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

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## Wednesday seminar

## Logic Seminar Talk 7 February 2024 17:00 hrs by Alexander Rabinovich at NUS

## This Week in Logic at CUNY

Rutgers Logic Seminar

Monday, Feb 5, 3:30pm, Rutgers University, Hill 705

Filippo Calderoni, Rutgers

The L-space conjecture and descriptive set theory

Logic and Metaphysics Workshop

Date: Monday, Feb 5, 4.15-6.15pm (NY time)

Room: Graduate Center Room 7395

*Title*: Some model theory for axiomatic theories of truth

*Abstract*: Tarski’s arithmetic is the complete theory of (N,+,x,Tr), where (N,+,x) is the standard model of arithmetic and Tr is the set of Gödel numbers of all true arithmetic sentences. An axiomatic theory of truth is an axiomatic subtheory of Tarski’s arithmetic. If (M,+,x,T) is a model of an axiomatic theory of truth, then we call T a truth class. In 1981, Kotlarski, Krajewski, and Lachlan proved that every completion of Peano’s arithmetic has a model that is expandable to a model with a truth class T that satisfies all biconditionals in Tarski’s definition of truth formalized in PA. If T is such a truth class, it assigns truth values to all sentences in the sense of M, standard and nonstandard. The proof showed that such truth classes can be quite pathological. For example, they may declare true some infinite disjunctions of the single sentence (0=1). In 2018, Enayat and Visser gave a much simplified model-theoretic proof, which opened the door for further investigations of nonstandard truths, and many interesting new results by many authors appeared. I will survey some of them, concentrating on their model-theoretic content.

- - - - Tuesday, Feb 6, 2024 - - - -

- - - - Wednesday, Feb 7, 2024 - - - -

The New York City Category Theory Seminar

Department of Computer Science

Department of Mathematics

The Graduate Center of The City University of New York

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

Speaker: ** Saeed Salehi, Univeristy of Tarbiz.**

Date and Time: ** Wednesday February 7, 2024, 11:00AM - 12:00 NOON. NOTICE SPECIAL TIME!!! ZOOM TALK!!! (see website for zoom link)**

Title:** On Chaitin's two HP's: (1) Heuristic Principle and (2) Halting Probability.**

Abstract: Two important achievements of Chaitin will be investigated: the Omega number, which is claimed to be the halting probability of input-free programs, and the heuristic principle, which is claimed to hold for program-size complexity. Chaitin's heuristic principle says that the theories cannot prove the heavier sentences; the sentences and the theories were supposedly weighed by various computational complexities, which all turned out to be wrong or incomplete. In this talk, we will introduce a weighting that is not based on any computational complexity but on the provability power of the theories, for which Chaitin's heuristic principle holds true. Also, we will show that the Omega number is not equal to the halting probability of the input-free programs and will suggest some methods for calculating this probability, if any.

- - - - Thursday, Feb 8, 2024 - - - -

- - - - Friday, Feb 9, 2024 - - - -

Speaker: Emma Dinowitz, Grad Center

CUNY Graduate Center

Friday, Feb 9, 12:30pm NY time, Room: 6494

**Tukey-top ultrafilters under UA**

In the first part of the talk, we will provide some background and motivation to study the Glavin property. In particular, we will present a recently discovered connection between the Galvin property and the Tukey order on ultrafilters. This is a joint result with Natasha Dobrinen. In the second part, we will introduce several diamond-like principles for ultrafilters, and prove some relations with the Galvin property. Finally, we use the Ultrapower Axiom to characterize the Galvin property in the known canonical inner models. The second and third part is joint work with Gabriel Goldberg.

CUNY Graduate Center

**Properties of Generic Algebraic Fields**

The algebraic field extensions of the rational numbers – equivalently, the subfields of the algebraic closure – naturally form a topological space homeomorphic to Cantor space. Consequently, one can speak of 'large' collections of such fields, in the sense of Baire category: collections that are comeager in the space. Under a standard definition, the *1-generic fields* form a comeager set in this space. Therefore, one may think of a property common to all 1-generic fields as a property that one might reasonably expect to be true of an arbitrarily chosen algebraic field.

We will present joint work with Eisenträger, Springer, and Westrick that proves several intriguing properties to be true of all 1-generic fields . First, in every such , both the subring of the integers and the subring of the algebraic integers of cannot be defined within by an existential formula, nor by a universal formula. (Subsequent work by Dittman and Fehm has shown that in fact these subrings are completely undefinable in these fields.) Next, for every presentation of every such , the *root set*

is always of low Turing degree relative to that presentation, but is essentially always undecidable relative to the presentation. Moreover, the set known as *Hilbert's Tenth Problem for *,

is exactly as difficult as , which is its restriction to single-variable polynomials. Finally, even the question of having infinitely many solutions,

is only as difficult as . These results are proven by using a forcing notion on the fields and showing that it is decidable whether or not a given condition forces a given polynomial to have a root, or to have infinitely many roots.

- - - - Monday, Feb 12, 2024 - - - -

Rutgers Logic Seminar

Monday, Feb 12, 3:30pm, Rutgers University, Hill 705

- - - - Tuesday, Feb 13, 2024 - - - -

MOPA

The Borel hierarchy gives a robust way to stratify the complexity of sets of countable structures and is intimately tied with definability in infinitary logic via the Lopez-Escobar theorem. However, what happens with sets axiomatizable in finitary first-order logic, such as the set of structures satisfying a given finitary first-order theory T? Is the complexity of the set of T's models in any way related to the quantifier complexity of the sentences axiomatizing it? In particular, if a theory T is not axiomatizable by a set of sentences of bounded quantifier complexity, can the set of models of T still be at a finite level of the Borel hierarchy?

In this talk, we will present results concerning these questions:

In joint work with Andrews, Gonzalez, Lempp, and Zhu we show that the set of models of a theory T is -complete if and only if T does not have an axiomatization by sentences of bounded quantifier complexity, answering the last question in the negative. We also characterize the Borel complexity of the set of models of complete theories in terms of their finitary axiomatizations. Our results suggest that infinitary logic does not provide any efficacy when defining first-order properties, a phenomenon already observed by Wadge and Keisler and, recently, rediscovered by Harrison-Trainor and Kretschmer using different techniques.

Combining our results with recent results by Enayat and Visser, we obtain that a large class of theories studied in the foundations of mathematics, sequential theories, have a maximal complicated set of models.

- - - - Wednesday, Feb 14, 2024 - - - -

- - - - Thursday, Feb 15, 2024 - - - -

- - - - Friday, Feb 16, 2024 - - - -

**Largeness notions**

Finite Ramsey Theorem states that fixed , there exists such that for each coloring of with colors, there is a homogeneous subset of of cardinality at least . Starting with the celebrated Paris-Harrington theorem, many Ramsey-like results have been studied using different largeness notions rather than the cardinality. I will introduce the largeness notion defined by Ketonen and Solovay based on fundamental sequences of ordinals. Then I will describe an alternative and more flexible largeness notion using blocks and barriers. If time allows, I will talk about how the latter can be used to study a more general Ramsey-like result.

CUNY Graduate Center

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@citytech.cuny.edu.

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

## Wednesday seminar

## This Week in Logic at CUNY

Rutgers Logic Seminar

Monday, Jan 29, 3:30pm, Rutgers University, Hill 705

Jenna Zomback, Maryland

Boundary actions of free semigroups

- - - - Tuesday, Jan 30, 2024 - - - -

- - - - Wednesday, Jan 31, 2024 - - - -

- - - - Thursday, Feb 1, 2024 - - - -

- - - - Friday, Feb 2, 2024 - - - -

CUNY Graduate Center

Friday, Feb 2, 12:30pm NY time, Room: 6494

CUNY Graduate Center

- - - - Monday, Feb 5, 2024 - - - -

Logic and Metaphysics Workshop

Date: Monday, Feb 5, 4.15-6.15pm (NY time)

Room: Graduate Center Room 7395

*Title*: Some model theory for axiomatic theories of truth

*Abstract*: Tarski’s arithmetic is the complete theory of (N,+,x,Tr), where (N,+,x) is the standard model of arithmetic and Tr is the set of Gödel numbers of all true arithmetic sentences. An axiomatic theory of truth is an axiomatic subtheory of Tarski’s arithmetic. If (M,+,x,T) is a model of an axiomatic theory of truth, then we call T a truth class. In 1981, Kotlarski, Krajewski, and Lachlan proved that every completion of Peano’s arithmetic has a model that is expandable to a model with a truth class T that satisfies all biconditionals in Tarski’s definition of truth formalized in PA. If T is such a truth class, it assigns truth values to all sentences in the sense of M, standard and nonstandard. The proof showed that such truth classes can be quite pathological. For example, they may declare true some infinite disjunctions of the single sentence (0=1). In 2018, Enayat and Visser gave a much simplified model-theoretic proof, which opened the door for further investigations of nonstandard truths, and many interesting new results by many authors appeared. I will survey some of them, concentrating on their model-theoretic content.

- - - - Tuesday, Feb 6, 2024 - - - -

- - - - Wednesday, Feb 7, 2024 - - - -

The New York City Category Theory Seminar

Department of Computer Science

Department of Mathematics

The Graduate Center of The City University of New York

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

Speaker: ** Saeed Salehi, Univeristy of Tarbiz.**

Date and Time: ** Wednesday February 7, 2024, 11:00AM - 12:00 NOON. NOTICE SPECIAL TIME!!! ZOOM TALK!!! (see website for zoom link)**

Title:** On Chaitin's two HP's: (1) Heuristic Principle and (2) Halting Probability.**

Abstract: Two important achievements of Chaitin will be investigated: the Omega number, which is claimed to be the halting probability of input-free programs, and the heuristic principle, which is claimed to hold for program-size complexity. Chaitin's heuristic principle says that the theories cannot prove the heavier sentences; the sentences and the theories were supposedly weighed by various computational complexities, which all turned out to be wrong or incomplete. In this talk, we will introduce a weighting that is not based on any computational complexity but on the provability power of the theories, for which Chaitin's heuristic principle holds true. Also, we will show that the Omega number is not equal to the halting probability of the input-free programs and will suggest some methods for calculating this probability, if any.

- - - - Thursday, Feb 8, 2024 - - - -

- - - - Friday, Feb 9, 2024 - - - -

CUNY Graduate Center

Friday, Feb 9, 12:30pm NY time, Room: 6494

CUNY Graduate Center

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@citytech.cuny.edu.

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

## 43rd Nankai Logic Colloquium

Hello everyone,

This week our weekly Nankai Logic Colloquium is going to be in the morning.

Our speaker this week will be Alexander S. Kechris from the California Institute of Technology. This talk is going to take place this Friday, Jan 26, from 9am to 10am(UTC+8, Beijing time).

The records of past talks can be accessed at https://space.bilibili.com/253421893.

Best Wishes,

Ming Xiao

## 7th Workshop on Generalised Baire Spaces

## Invitation to Logic Seminar 31 January 2024 17:00 hrs at NUS by Yu Liang

## This Week in Logic at CUNY

- - - - Monday, Jan 22, 2024 - - - -

Rutgers Logic Seminar

Monday, Dec 11, 3:30pm, Rutgers University, Hill 705

Will Boney (Texas State)

- - - - Tuesday, Jan 23, 2024 - - - -

- - - - Wednesday, Jan 24, 2024 - - - -

- - - - Thursday, Jan 25, 2024 - - - -

- - - - Friday, Jan 26, 2024 - - - -

Memorial Lectures for Martin Davis

January 26, 2024

Courant Institute

All are welcome to attend this special event in memory of Professor Martin Davis.

There will be three lectures on his work from 1:00 - 2:30 pm, a memorial for Martin

and Virginia Davis from 2:45 - 3:45 pm, and a reception afterwards from 4-6 pm.

Preregistration is requested, ideally by January 15, using the website

https://cims.nyu.edu/dynamic/conferences/davis-memorial/

Next Week in Logic at CUNY:

- - - - Monday, Jan 29, 2024 - - - -

- - - - Tuesday, Jan 30, 2024 - - - -

- - - - Wednesday, Jan 31, 2024 - - - -

- - - - Thursday, Feb 1, 2024 - - - -

- - - - Friday, Feb 2, 2024 - - - -

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@citytech.cuny.edu.

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

## Wednesday seminar

## Second Wrocław Logic Conference, Wrocław, 31 May to 2 Jun, 2024

## Set Theory and Topology Seminar 23.01.2024 Łukasz Mazurkiewicz

**Łukasz Mazurkiewicz**

Abstract.

About 15 minutes before the seminar we invite you for coffee and a chat to social room.

https://settheory.pwr.edu.pl/

http://www.math.uni.wroc.pl/seminarium/topologia

## Urgent Announcement of Nankai Logic Colloquium: change to Voov (Tencent meeting)

Hello everyone,

Sorry, we have changed the meeting software to Voov (Tencent meeting) because the our Zoom account has been banned.

Please download Voov (Tencent meeting) from the following link:

https://voovmeeting.com/download-center.html?from=1002

the attachment is the Manual for using Voov (Tencent meeting)

Best Wishes,

Ming Xiao

## Set Theory in the United Kingdom, London, February 15, 2024

## 42nd Nankai Logic Colloquium

Hello everyone,

This week our weekly Nankai Logic Colloquium is going to be in the afternoon.

Our speaker this week will be Gianluca Paolini from the University of Turin. This talk is going to take place this Friday, Jan 19, from 4pm to 5pm(UTC+8, Beijing time).

The records of past talks can be accessed at https://space.bilibili.com/253421893.

Best Wishes,

Ming Xiao

## Cross-Alps Logic Seminar for World Logic Day (speaker: Charles Steinhorn)

On
Friday 19.01.2023 at 16:00

on
the occasion of World Logic Day 2024, a special session of the
Cross-Alps Logic Seminars will take place, with special guest

**Charles
Steinhorn** (Vassar College)

who
will give a talk on

**O-minimality
as a framework for tame mathematical economics**

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
vincenzo.dimonte [at] uniud [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 2022 'Models, sets and classification'.

## Wednesday seminar

## Logic Seminar at NUS Wed 17.01.2024 17:00 hrs by Tatsuta Makoto

## 41st Nankai Logic Colloquium

Hello everyone,

This week our weekly Nankai Logic Colloquium is going to be in the afternoon.

Our speaker this week will be Felipe Garcia-Ramos from Jagiellonian University. This talk is going to take place this Friday, Jan 12, from 4pm to 5pm(UTC+8, Beijing time).

The records of past talks can be accessed at https://space.bilibili.com/253421893.

Best Wishes,

Ming Xiao

## KGRC Talks - January 8-12

## set theory and topology seminar 9.01.2024 Piotr Borodulin-Nadzieja

**Piotr Borodulin-Nadzieja**

Abstract.

About 15 minutes before the seminar we invite you for coffee and a chat to social room.

https://settheory.pwr.edu.pl/

http://www.math.uni.wroc.pl/seminarium/topologia

## Wednesday seminar

## 40th Nankai Logic Colloquium

Hello everyone,

This week our weekly Nankai Logic Colloquium is going to be in the afternoon.

Our speaker this week will be Steve Jackson from the University of North Texas. This talk is going to take place this Friday, Jan 05, from 4pm to 5pm(UTC+8, Beijing time).

The records of past talks can be accessed at https://space.bilibili.com/253421893.

Best Wishes,

Ming Xiao

## Wednesday seminar

## Stationary Sets and Algebra, VCU, May 20, 2024

## 39th Nankai Logic Colloquium

Hello everyone,

This week our weekly Nankai Logic Colloquium is going to be in the afternoon.

Our speaker this week will be Yinhe Peng from the Academy of Mathematics and Systems Science, CAS. This talk is going to take place this Friday, Dec 29, from 4pm to 5pm(UTC+8, Beijing time).

The records of past talks can be accessed at https://space.bilibili.com/253421893.

Best Wishes,

Ming Xiao

## BLAST, North Texas, April 6-9, 2024

## Wednesday seminar

## Set Theory Seminar 19.12.2023 Aleksander Cieślak

**Aleksander Cieślak**

Abstract.

About 15 minutes before the seminar we invite you for coffee and a chat to social room.

https://settheory.pwr.edu.pl/

http://www.math.uni.wroc.pl/seminarium/topologia

## 38th Nankai Logic Colloquium

Hello everyone,

This week our weekly Nankai Logic Colloquium is going to be in the morning.

Our speaker this week will be Forte Shinko from the University of California, Berkeley. This talk is going to take place this Friday, Dec 15, from 9am to 10am(UTC+8, Beijing time).

We are pausing our colloquium for once next week, due to the Annual Meeting of the Chinese Mathematical Society 2023. The Colloquium will be resumed Dec. 29.

Abstract: A countable discrete group is exact if it has a free action on Cantor space which is measure-hyperfinite, that is, for every Borel probability measure on Cantor space, there is a conull set on which the orbit equivalence relation is hyperfinite. For an exact group, it is known that the generic action on Cantor space is measure-hyperfinite, and it is open as to whether the generic action is hyperfinite; an exact group for which the generic action is not hyperfinite would resolve a long-standing open conjecture about whether measure-hyperfiniteness and hyperfiniteness are equivalent. We show that for any countable discrete group with finite asymptotic dimension, its generic action on Cantor space is hyperfinite. This is joint work with Sumun Iyer.

The records of past talks can be accessed from https://space.bilibili.com/253421893.

Best Wishes,

Ming Xiao

## (KGRC) one talk TOMORROW, December 12, two talks on Thursday, December 14

## This Week in Logic at CUNY

Rutgers Logic Seminar

Monday, Dec 11, 3:30pm, Rutgers University, Hill 705

Preserving the Ultrapower Axiom in forcing extensions

Logic and Metaphysics Workshop

Date: Monday, Dec 11, 4.15-6.15pm (NY time)

Room: Graduate Center Room 4419

Title: The logic of social choice

Abstract: Logic entered social choice theory through Kenneth Arrow who was a student of the logician Alfred Tarski at City College of New York. Arrow’s impossibility result, which was axiomatic in nature, showed that there is no rational procedure to define the popular choice when there are three or more candidates. Arrow’s result led to a rich field. However, subsequent work has concentrated on what happens when voters face a slate of three or more candidates. There is not enough work on a theory of candidate slates themselves. Thus an election with just Donald Trump and Joe Biden is seen as unproblematic since there are only two candidates. The actual quality of the candidates does not matter. We will propose a method which depends on the actual quality of a candidate. Then it becomes a dominant game theoretic strategy for each party to nominate as good a candidate as possible. The goodness of a candidate is defined in terms of a dot product of two vectors: the candidate’s position and the position of a typical voter.

- - - - Tuesday, Dec 12, 2023 - - - -

Models of Peano Arithmetic (MOPA)

Tuesday, Dec 12, 1:00pm

Virtual (email Victoria Gitman vgitman@gmail.com for meeting id)

Karel Hrbáček, CUNY**Multi-level nonstandard analysis, the axiom of choice, and recent work of R. Jin**

Model-theoretic frameworks for nonstandard methods require the existence of nonprincipal ultrafilters over N, a strong form of the Axiom of Choice (AC). While AC is instrumental in many abstract areas of mathematics, its use in infinitesimal calculus or number theory should not be necessary.

In the paper KH and M. G. Katz, Infinitesimal analysis without the Axiom of Choice, Ann. Pure Applied Logic 172, 6 (2021), https://arxiv.org/abs/2009.04980, we have formulated SPOT, a theory in the language that has, in addition to membership, a unary predicate 'is standard.' The theory extends ZF by three simple axioms, Transfer, Nontriviality and Standard Part, that reflect the insights of Leibniz. It is a subtheory of the nonstandard set theories IST and HST, but unlike them, it is a conservative extension of ZF. Arguments carried out in SPOT thus do not depend on any form of AC. Infinitesimal calculus can be developed in SPOT. A stronger theory SCOT is a conservative extension of ZF + Dependent Choice. It is suitable for handling such features as an infinitesimal approach to the Lebesgue measure.

Renling Jin recently gave a groundbreaking nonstandard proof of Szemeredi's theorem in a model-theoretic framework that has three levels of infinity. I will formulate and motivate SPOTS, a multi-level version of SPOT, carry out Jin's proof of Ramsey's theorem in SPOTS, and discuss how his proof of Szemeredi's theorem can be developed in it.

While it is still open whether SPOTS is conservative over ZF, SCOTS (the multi-level version of SCOT) is a conservative extension of ZF + Dependent Choice.

- - - - Wednesday, Dec 13, 2023 - - - -

- - - - Thursday, Dec 14, 2023 - - - -

* EXAMS WEEK CUNY GRADUATE CENTER *

- - - - Friday, Dec 15, 2023 - - - -

- - - - Monday, Dec 18, 2023 - - - -

- - - - Tuesday, Dec 19, 2023 - - - -

- - - - Wednesday, Dec 20, 2023 - - - -

- - - - Thursday, Dec 21, 2023 - - - -

- - - - Friday, Dec 22, 2023 - - - -

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@citytech.cuny.edu.

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

## Wednesday seminar

## 37th Nankai Logic Colloquium

Hello everyone,

This week our weekly Nankai Logic Colloquium is going to be in the morning.

Our speaker this week will be Wei He from Nanjing Normal University. This talk is going to take place this Friday, Dec 08, from 9am to 10am(UTC+8, Beijing time).

_____________________________________________________________________________________________________

The records of past talks can be accessed from https://space.bilibili.com/253421893.

Best Wishes,

Ming Xiao

## (KGRC) CORRECTED: the future of KGRC announcements, plus three talks

## UPDATE - This Week in Logic at CUNY

Monday, Dec 4, 3:30pm, Rutgers University, Hill 705

The computable model theory of forcing

Logic and Metaphysics Workshop

Date: Monday, Dec 4, 4.15-6.15pm (NY time)

Room: Graduate Center Room 4419

James Walsh (NYU)

Title: Use and mention in formal languages

Abstract: Quine’s distinction between use and mention is one of the cornerstones of analytic philosophy. The distinction is typically motivated with examples from natural language, but Quine also applied the distinction to the formal languages studied in mathematical logic. I will argue that such expressions are not used in Quine’s sense, so the distinction cannot appropriately be applied to them. Accordingly, the standard practice of placing quotation marks around expressions of formal languages is incorrect. This technical point serves as a springboard for discussing the role that formal languages play in mathematical logic.

- - - - Tuesday, Dec 5, 2023 - - - -

Models of Peano Arithmetic (MOPA)

Tuesday, Dec 5, 1:00pm

Virtual (email Victoria Gitman vgitman@gmail.com for meeting id)

**Simplest model properties for Peano Arithmetic: On a question of Montalban and Rossegger**

As famously shown by Scott, every countable structure can be characterized, up to isomorphism, by a sentence of infinitary language which allows for conjunctions and disjunctions over arbitrary countable families of formulae (over finitely many variables). Formulae of this language can be naturally assigned ranks based on the number of alternations of existential connectives (disjunctions and existential quantifiers) with universal ones (conjunctions and universal quantifiers). This gives rise to a natural complexity measure for countable models: the Scott rank of a model is the least such that can be uniquely characterized by a sentence of rank (and starting from the universal quantifier). The developments of computable model theory witness that the Scott rank is a very robust notion integrating other well established tools from descriptive set theory, model theory and computability.

In 'The Structural Complexity of Models of Arithmetic' Antonio Montalban and Dino Rossegger pioneered the Scott analysis of models of Peano Arithmetic. They characterized the Scott spectrum of completions PA , i.e. the set of ordinals which are Scott ranks of countable models of a given completion of PA. A particularly intriguing outcome of their analysis is that PA has exactly one model of the least rank, the standard model, and the Scott rank of every other model is infinite. Additionally they studied the connections between Scott ranks and model-theoretical properties of models, such as recursive saturation and atomicity, raising an open question: is there a non-atomic homogeneous model of PA of Scott rank ?

In the talk we answer the above question to the negative, showing that the nonstandard models of PA or rank are exactly the nonstandard prime models. This witness another peculiar property of PA: not only it has the simplest model, but also its every completion has a unique model of the least Scott rank. This is joint work with Patryk Szlufik.

- - - - Wednesday, Dec 6, 2023 - - - -

- - - - Thursday, Dec 7, 2023 - - - -

- - - - Friday, Dec 8, 2023 - - - -

Every archimedean real closed field is rigid, i.e., has no nontrivial automorphisms. What happens in the non-archimedean case? Shelah showed it is consistent that there are uncountable rigid non-archimedean real closed fields. Enayat asked what happens in the countable case. I believe the question is even interesting in the finite transcendence degree case. In this talk I will describe Shelah's proof and discuss some interesting phenomenon that arises even in transcendence degree 2.

CUNY Graduate Center

**Michael Benedikt**, Oxford University**Nested Data, Views, and Gaifman Coordinization**

I will begin with an overview of how implicit definition, and variations of Beth's definability theorem, arise in relational databases, particularly in the context of view rewriting.

We then turn from relational databases to nested relational databases, a model of hierarchical data - 'objects' - where tables can contain tuples whose components are again tables. There is a standard transformation language for this data model, the Nested Relational Calculus (NRC). We show that a variant of Gaifman's coordinatization theorem plays a role in lieu of Beth's theorem, allowing one to generate NRC transformations from several kinds of implicit specifications. We discuss how to generate transformations effectively from specifications, which requires the development of proof-theoretic methods for implicit definability over nested sets.

This is joint work with Ceclia Pradic and Christoph Wernhard.

- - - - Monday, Dec 11, 2023 - - - -

Rutgers Logic Seminar

Monday, Dec 11, 3:30pm, Rutgers University, Hill 705

Preserving the Ultrapower Axiom in forcing extensions

Logic and Metaphysics Workshop

Date: Monday, Dec 11, 4.15-6.15pm (NY time)

Room: Graduate Center Room 4419

Title: The logic of social choice

Abstract: Logic entered social choice theory through Kenneth Arrow who was a student of the logician Alfred Tarski at City College of New York. Arrow’s impossibility result, which was axiomatic in nature, showed that there is no rational procedure to define the popular choice when there are three or more candidates. Arrow’s result led to a rich field. However, subsequent work has concentrated on what happens when voters face a slate of three or more candidates. There is not enough work on a theory of candidate slates themselves. Thus an election with just Donald Trump and Joe Biden is seen as unproblematic since there are only two candidates. The actual quality of the candidates does not matter. We will propose a method which depends on the actual quality of a candidate. Then it becomes a dominant game theoretic strategy for each party to nominate as good a candidate as possible. The goodness of a candidate is defined in terms of a dot product of two vectors: the candidate’s position and the position of a typical voter.

- - - - Tuesday, Dec 12, 2023 - - - -

Models of Peano Arithmetic (MOPA)

Tuesday, Dec 12, 1:00pm

Virtual (email Victoria Gitman vgitman@gmail.com for meeting id)

Karel Hrbáček, CUNY**Multi-level nonstandard analysis, the axiom of choice, and recent work of R. Jin**

Model-theoretic frameworks for nonstandard methods require the existence of nonprincipal ultrafilters over N, a strong form of the Axiom of Choice (AC). While AC is instrumental in many abstract areas of mathematics, its use in infinitesimal calculus or number theory should not be necessary.

In the paper KH and M. G. Katz, Infinitesimal analysis without the Axiom of Choice, Ann. Pure Applied Logic 172, 6 (2021), https://arxiv.org/abs/2009.04980, we have formulated SPOT, a theory in the language that has, in addition to membership, a unary predicate 'is standard.' The theory extends ZF by three simple axioms, Transfer, Nontriviality and Standard Part, that reflect the insights of Leibniz. It is a subtheory of the nonstandard set theories IST and HST, but unlike them, it is a conservative extension of ZF. Arguments carried out in SPOT thus do not depend on any form of AC. Infinitesimal calculus can be developed in SPOT. A stronger theory SCOT is a conservative extension of ZF + Dependent Choice. It is suitable for handling such features as an infinitesimal approach to the Lebesgue measure.

Renling Jin recently gave a groundbreaking nonstandard proof of Szemeredi's theorem in a model-theoretic framework that has three levels of infinity. I will formulate and motivate SPOTS, a multi-level version of SPOT, carry out Jin's proof of Ramsey's theorem in SPOTS, and discuss how his proof of Szemeredi's theorem can be developed in it.

While it is still open whether SPOTS is conservative over ZF, SCOTS (the multi-level version of SCOT) is a conservative extension of ZF + Dependent Choice.

- - - - Wednesday, Dec 13, 2023 - - - -

- - - - Thursday, Dec 14, 2023 - - - -

* EXAMS WEEK CUNY GRADUATE CENTER *

- - - - Friday, Dec 15, 2023 - - - -

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@citytech.cuny.edu.

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

## Wednesday seminar

## Logic Seminar 5 Dec 2023 15:30 hrs at NUS by Lu Qi

## This Week in Logic at CUNY

Monday, Dec 4, 3:30pm, Rutgers University, Hill 705

The computable model theory of forcing

Logic and Metaphysics Workshop

Date: Monday, Dec 4, 4.15-6.15pm (NY time)

Room: Graduate Center Room 4419

James Walsh (NYU)

Title: Use and mention in formal languages

Abstract: Quine’s distinction between use and mention is one of the cornerstones of analytic philosophy. The distinction is typically motivated with examples from natural language, but Quine also applied the distinction to the formal languages studied in mathematical logic. I will argue that such expressions are not used in Quine’s sense, so the distinction cannot appropriately be applied to them. Accordingly, the standard practice of placing quotation marks around expressions of formal languages is incorrect. This technical point serves as a springboard for discussing the role that formal languages play in mathematical logic.

- - - - Tuesday, Dec 5, 2023 - - - -

Models of Peano Arithmetic (MOPA)

Tuesday, Dec 5, 1:00pm

Virtual (email Victoria Gitman vgitman@gmail.com for meeting id)

**Simplest model properties for Peano Arithmetic: On a question of Montalban and Rossegger**

As famously shown by Scott, every countable structure can be characterized, up to isomorphism, by a sentence of infinitary language which allows for conjunctions and disjunctions over arbitrary countable families of formulae (over finitely many variables). Formulae of this language can be naturally assigned ranks based on the number of alternations of existential connectives (disjunctions and existential quantifiers) with universal ones (conjunctions and universal quantifiers). This gives rise to a natural complexity measure for countable models: the Scott rank of a model is the least such that can be uniquely characterized by a sentence of rank (and starting from the universal quantifier). The developments of computable model theory witness that the Scott rank is a very robust notion integrating other well established tools from descriptive set theory, model theory and computability.

In 'The Structural Complexity of Models of Arithmetic' Antonio Montalban and Dino Rossegger pioneered the Scott analysis of models of Peano Arithmetic. They characterized the Scott spectrum of completions PA , i.e. the set of ordinals which are Scott ranks of countable models of a given completion of PA. A particularly intriguing outcome of their analysis is that PA has exactly one model of the least rank, the standard model, and the Scott rank of every other model is infinite. Additionally they studied the connections between Scott ranks and model-theoretical properties of models, such as recursive saturation and atomicity, raising an open question: is there a non-atomic homogeneous model of PA of Scott rank ?

In the talk we answer the above question to the negative, showing that the nonstandard models of PA or rank are exactly the nonstandard prime models. This witness another peculiar property of PA: not only it has the simplest model, but also its every completion has a unique model of the least Scott rank. This is joint work with Patryk Szlufik.

- - - - Wednesday, Dec 6, 2023 - - - -

- - - - Thursday, Dec 7, 2023 - - - -

- - - - Friday, Dec 8, 2023 - - - -

Every archimedean real closed field is rigid, i.e., has no nontrivial automorphisms. What happens in the non-archimedean case? Shelah showed it is consistent that there are uncountable rigid non-archimedean real closed fields. Enayat asked what happens in the countable case. I believe the question is even interesting in the finite transcendence degree case. In this talk I will describe Shelah's proof and discuss some interesting phenomenon that arises even in transcendence degree 2.

CUNY Graduate Center

**Michael Benedikt**, Oxford University**Nested Data, Views, and Gaifman Coordinization**

I will begin with an overview of how implicit definition, and variations of Beth's definability theorem, arise in relational databases, particularly in the context of view rewriting.

We then turn from relational databases to nested relational databases, a model of hierarchical data - 'objects' - where tables can contain tuples whose components are again tables. There is a standard transformation language for this data model, the Nested Relational Calculus (NRC). We show that a variant of Gaifman's coordinatization theorem plays a role in lieu of Beth's theorem, allowing one to generate NRC transformations from several kinds of implicit specifications. We discuss how to generate transformations effectively from specifications, which requires the development of proof-theoretic methods for implicit definability over nested sets.

This is joint work with Ceclia Pradic and Christoph Wernhard.

- - - - Monday, Dec 11, 2023 - - - -

Rutgers Logic Seminar

Monday, Dec 11, 3:30pm, Rutgers University, Hill 705

Preserving the Ultrapower Axiom in forcing extensions

- - - - Tuesday, Dec 12, 2023 - - - -

Models of Peano Arithmetic (MOPA)

Tuesday, Dec 12, 1:00pm

Virtual (email Victoria Gitman vgitman@gmail.com for meeting id)

Karel Hrbáček, CUNY**Multi-level nonstandard analysis, the axiom of choice, and recent work of R. Jin**

Model-theoretic frameworks for nonstandard methods require the existence of nonprincipal ultrafilters over N, a strong form of the Axiom of Choice (AC). While AC is instrumental in many abstract areas of mathematics, its use in infinitesimal calculus or number theory should not be necessary.

In the paper KH and M. G. Katz, Infinitesimal analysis without the Axiom of Choice, Ann. Pure Applied Logic 172, 6 (2021), https://arxiv.org/abs/2009.04980, we have formulated SPOT, a theory in the language that has, in addition to membership, a unary predicate 'is standard.' The theory extends ZF by three simple axioms, Transfer, Nontriviality and Standard Part, that reflect the insights of Leibniz. It is a subtheory of the nonstandard set theories IST and HST, but unlike them, it is a conservative extension of ZF. Arguments carried out in SPOT thus do not depend on any form of AC. Infinitesimal calculus can be developed in SPOT. A stronger theory SCOT is a conservative extension of ZF + Dependent Choice. It is suitable for handling such features as an infinitesimal approach to the Lebesgue measure.

Renling Jin recently gave a groundbreaking nonstandard proof of Szemeredi's theorem in a model-theoretic framework that has three levels of infinity. I will formulate and motivate SPOTS, a multi-level version of SPOT, carry out Jin's proof of Ramsey's theorem in SPOTS, and discuss how his proof of Szemeredi's theorem can be developed in it.

While it is still open whether SPOTS is conservative over ZF, SCOTS (the multi-level version of SCOT) is a conservative extension of ZF + Dependent Choice.

- - - - Wednesday, Dec 13, 2023 - - - -

- - - - Thursday, Dec 14, 2023 - - - -

* EXAMS WEEK CUNY GRADUATE CENTER *

- - - - Friday, Dec 15, 2023 - - - -

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@citytech.cuny.edu.

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

## Set Theory and Topology Seminar 5.12.2023 Daria Perkowska

**Daria Perkowska**

Abstract.

About 15 minutes before the seminar we invite you for coffee and a chat to social room.

https://settheory.pwr.edu.pl/

http://www.math.uni.wroc.pl/seminarium/topologia

## 36th Nankai Logic Colloquium

Hello everyone,

This week our weekly Nankai Logic Colloquium is going to be in the afternoon.

Our speaker this week will be Victor Hugo Yanez from Nanjing Normal University. This talk is going to take place this Friday, Dec 01, from 4pm to 5pm(UTC+8, Beijing time).

_____________________________________________________________________________________________________

Title ：The 36th Nankai Logic Colloquium --Victor Hugo Yañez

Time ：16:00pm, Dec. 1, 2023(Beijing Time)

Zoom Number ： 671 670 2069

Passcode ： 773654

Link ：https://us05web.zoom.us/j/6716702069?pwd=mhCy9U60VrE8F6YSCOxOlGxIDPFTgx.1&omn=89006488717

_____________________________________________________________________

Best wishes,

Ming Xiao

## (KGRC) two seminar talks Thursday, November 30

## Cross-Alps Logic Seminar (speaker: Zoltán Vidnyánszky)

**Zoltán Vidnyánszky**(Eötvös Loránd University)

*Homomorphisms in the choiceless world*## This Week in Logic at CUNY

Logic and Metaphysics Workshop

Date: Monday, Nov 27, 4.15-6.15pm (NY time)

Room: Graduate Center Room 4419

Title: Truth with and without satisfaction

Abstract: The talk addresses a quite natural situation in mathematics. When one needs to define a concept and it is not possible to do a direct recursion on the concept itself, what one does is the next best thing which is to perform recursion on a related concept of which the original given concept can be shown to be a special case. Tarski, in his celebrated paper on “The Concept of Truth in Formalized Languages”, cannot give a definition of truth performing direct recursion on the concept of truth itself. Consequently, he settles on a definition in terms of satisfaction. Following Kit Fine and Timothy McCarthy, “Truth without Satisfaction”, I raise the issue of whether such an indirect procedure of giving a definition of truth is necessary or maybe an alternative definition of truth can be given without going through the related concept of satisfaction. My talk will investigate both certain technical and philosophical aspects of the two sets of formal constraints to defining truth with and without satisfaction.

- - - - Tuesday, Nov 28, 2023 - - - -

- - - - Wednesday, Nov 29, 2023 - - - -

The New York City Category Theory Seminar

Department of Computer Science

Department of Mathematics

The Graduate Center of The City University of New York

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

Date and Time: Wednesday November 29, 2023, 7:00 - 8:30 PM. ZOOM TALK.

**A categorical semantics for neural networks.**

- - - - Thursday, Nov 30, 2023 - - - -

- - - - Friday, Dec 1, 2023 - - - -

Rehana Patel Wesleyan University

CUNY Graduate Center

**James Walsh**, New York University**Is the consistency operator canonical?**

It is a well-known empirical phenomenon that natural axiomatic theories are well-ordered by consistency strength. The restriction to natural theories is necessary; using ad-hoc techniques (such as self-reference and Rosser orderings) one can exhibit non-linearity and ill-foundedness in the consistency strength hierarchy. What explains the contrast between natural theories and axiomatic theories in general?

Our approach to this problem is inspired by work on an analogous problem in recursion theory. The natural Turing degrees are well-ordered by Turing reducibility, yet the Turing degrees in general are neither linearly ordered nor well-founded, as ad-hoc techniques (such as the priority method) bear out. Martin's Conjecture, which is still unresolved, is a proposed explanation for this phenomenon. In particular, Martin’s Conjecture specifies a way in which the Turing jump is canonical.

After discussing Martin’s Conjecture, we will formulate analogous proof-theoretic hypotheses according to which the consistency operator is canonical. We will then discuss results - both positive and negative - within this framework. Some of these results were obtained jointly with Antonio Montalbán.

- - - - Monday, Dec 4, 2023 - - - -

Monday, Dec 4, 3:30pm, Rutgers University, Hill 705

The computable model theory of forcing

Logic and Metaphysics Workshop

Date: Monday, Dec 4, 4.15-6.15pm (NY time)

Room: Graduate Center Room 4419

James Walsh (NYU)

Title: Use and mention in formal languages

Abstract: Quine’s distinction between use and mention is one of the cornerstones of analytic philosophy. The distinction is typically motivated with examples from natural language, but Quine also applied the distinction to the formal languages studied in mathematical logic. I will argue that such expressions are not used in Quine’s sense, so the distinction cannot appropriately be applied to them. Accordingly, the standard practice of placing quotation marks around expressions of formal languages is incorrect. This technical point serves as a springboard for discussing the role that formal languages play in mathematical logic.

- - - - Tuesday, Dec 5, 2023 - - - -

Models of Peano Arithmetic (MOPA)

Tuesday, Dec 5, 1:00pm

Virtual (email Victoria Gitman vgitman@gmail.com for meeting id)

Simplest model properties for Peano Arithmetic: On a question of Montalban and Rossegger

- - - - Wednesday, Dec 6, 2023 - - - -

- - - - Thursday, Dec 7, 2023 - - - -

- - - - Friday, Dec 8, 2023 - - - -

Every archimedean real closed field is rigid, i.e., has no nontrivial automorphisms. What happens in the non-archimedean case? Shelah showed it is consistent that there are uncountable rigid non-archimedean real closed fields. Enayat asked what happens in the countable case. I believe the question is even interesting in the finite transcendence degree case. In this talk I will describe Shelah's proof and discuss some interesting phenomenon that arises even in transcendence degree 2.

CUNY Graduate Center

Beth definability and nested relations

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@citytech.cuny.edu.

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

## Set Theory and Topology Seminar 28.11.2023 Jarosław Swaczyna

**Jarosław Swaczyna **(Łódź University of Technology)

Abstract.

About 15 minutes before the seminar we invite you for coffee and a chat to social room.

https://settheory.pwr.edu.pl/

http://www.math.uni.wroc.pl/seminarium/topologia

## Wednesday seminar

## (KGRC) videos, and the Set Theory Seminar talk this Thursday, November 23

## UPDATE: This Week in Logic at CUNY

Rutgers Logic Seminar

Monday, Nov 20, 3:30pm, Rutgers University, Hill 705

Logic and Metaphysics Workshop

Date: Monday, Nov 20, 4.15-6.15pm (NY time)

Room: Graduate Center Room 4419

Marian Călborean (Bucharest).

Title: Vagueness and Frege

Abstract: A constant of Frege’s writing is his rejection of indeterminate predicates in natural language. I follow Frege’s remarks on vagueness from the early “Begriffsschrift” to his mature works, drawing parallels with contemporary theories of vagueness. I critically examine Frege’s arguments for the inconsistency of natural language and argue that the inability to accommodate vagueness and precision in his mature ontology and semantics is mainly due to heuristic rules which he took as essential, not to a deep problem in his fundamental apparatus.

- - - - Tuesday, Nov 21, 2023 - - - -

Tuesday, Nov 21, 12:00pm

Virtual (email Victoria Gitman vgitman@gmail.com for meeting id)

Saeideh Bahrami, Institute for Research in Fundamental Sciences**-small submodels of countable models of arithmetic**

There has been a long tradition in the model theory of arithmetic of attributing the combinatorial properties of *cardinal numbers* in set theory to *initial* segments. Considering that the most basic use of cardinal numbers is to assign *cardinality* to sets, we can adapt a similar notion in models of arithmetic in the following way: for a given initial segment of any model of a fragment of arithmetic, say I, a subset of is called *I-small* if there exists a coded bijection in such that the range of the restriction of to is equal to . It turns out that for a given countable nonstandard model of I, when I is a strong cut, any -small -elementary submodel of contains , and inherits some good properties of . In this talk, we are going to review such properties through self-embeddings of .

- - - - Wednesday, Nov 22, 2023 - - - -

The New York City Category Theory Seminar

Department of Computer Science

Department of Mathematics

The Graduate Center of The City University of New York

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

**Pedro Sota, TBA.**

Date and Time:

~~Wednesday November 22, 2023, 7:00 - 8:30 PM. ZOOM TALK.~~ CANCELLED

- - - - Thursday, Nov 23, 2023 - - - -

*** Graduate Center Closed (Thanksgiving) ***

- - - - Friday, Nov 24, 2023 - - - -

- - - - Monday, Nov 27, 2023 - - - -

Logic and Metaphysics Workshop

Date: Monday, Nov 20, 4.15-6.15pm (NY time)

Room: Graduate Center Room 4419

Title: Truth with and without satisfaction

Abstract: The talk addresses a quite natural situation in mathematics. When one needs to define a concept and it is not possible to do a direct recursion on the concept itself, what one does is the next best thing which is to perform recursion on a related concept of which the original given concept can be shown to be a special case. Tarski, in his celebrated paper on “The Concept of Truth in Formalized Languages”, cannot give a definition of truth performing direct recursion on the concept of truth itself. Consequently, he settles on a definition in terms of satisfaction. Following Kit Fine and Timothy McCarthy, “Truth without Satisfaction”, I raise the issue of whether such an indirect procedure of giving a definition of truth is necessary or maybe an alternative definition of truth can be given without going through the related concept of satisfaction. My talk will investigate both certain technical and philosophical aspects of the two sets of formal constraints to defining truth with and without satisfaction.

- - - - Tuesday, Nov 28, 2023 - - - -

- - - - Wednesday, Nov 29, 2023 - - - -

The New York City Category Theory Seminar

Department of Computer Science

Department of Mathematics

The Graduate Center of The City University of New York

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

Date and Time: Wednesday November 29, 2023, 7:00 - 8:30 PM. ZOOM TALK.

- - - - Thursday, Nov 30, 2023 - - - -

- - - - Friday, Dec 1, 2023 - - - -

Rehana Patel Wesleyan University

CUNY Graduate Center

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

(site designed, built & maintained by Victoria Gitman)

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

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## 35th Nankai Logic Colloquium

Hello everyone,

This week our weekly Nankai Logic Colloquium is going to be in the afternoon.

Our speaker this week will be Kazuyuki Tanaka from the Beijing Institute of Mathematical Sciences and Applications. This talk is going to take place this Friday, Nov 24, from 4pm to 5pm(UTC+8, Beijing time).

___________________________________________________________________________________________________________________________________________________

Title ：The 35th Nankai Logic Colloquium --Kazuyuki Tanaka

Time ：16:00pm, Nov. 24, 2023(Beijing Time)

Zoom Number ：847 0296 7631

Passcode ：547555

Link ：https://zoom.us/j/84702967631?pwd=IApaBiX5Cqv58tVez39772LJdtHpfF.1

_____________________________________________________________________

Best wishes,

Ming Xiao

## This Week in Logic at CUNY

Rutgers Logic Seminar

Monday, Nov 20, 3:30pm, Rutgers University, Hill 705

Logic and Metaphysics Workshop

Date: Monday, Nov 20, 4.15-6.15pm (NY time)

Room: Graduate Center Room 4419

Marian Călborean (Bucharest).

Title: Vagueness and Frege

Abstract: A constant of Frege’s writing is his rejection of indeterminate predicates in natural language. I follow Frege’s remarks on vagueness from the early “Begriffsschrift” to his mature works, drawing parallels with contemporary theories of vagueness. I critically examine Frege’s arguments for the inconsistency of natural language and argue that the inability to accommodate vagueness and precision in his mature ontology and semantics is mainly due to heuristic rules which he took as essential, not to a deep problem in his fundamental apparatus.

- - - - Tuesday, Nov 21, 2023 - - - -

Tuesday, Nov 21, 1:00pm

Virtual (email Victoria Gitman vgitman@gmail.com for meeting id)

Saeideh Bahrami, Institute for Research in Fundamental Sciences**-small submodels of countable models of arithmetic**

There has been a long tradition in the model theory of arithmetic of attributing the combinatorial properties of *cardinal numbers* in set theory to *initial* segments. Considering that the most basic use of cardinal numbers is to assign *cardinality* to sets, we can adapt a similar notion in models of arithmetic in the following way: for a given initial segment of any model of a fragment of arithmetic, say I, a subset of is called *I-small* if there exists a coded bijection in such that the range of the restriction of to is equal to . It turns out that for a given countable nonstandard model of I, when I is a strong cut, any -small -elementary submodel of contains , and inherits some good properties of . In this talk, we are going to review such properties through self-embeddings of .

- - - - Wednesday, Nov 22, 2023 - - - -

The New York City Category Theory Seminar

Department of Computer Science

Department of Mathematics

The Graduate Center of The City University of New York

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

**Pedro Sota, TBA.**

Date and Time:

**Wednesday November 22, 2023, 7:00 - 8:30 PM. ZOOM TALK.**

- - - - Thursday, Nov 23, 2023 - - - -

*** Graduate Center Closed (Thanksgiving) ***

- - - - Friday, Nov 24, 2023 - - - -

- - - - Monday, Nov 27, 2023 - - - -

Logic and Metaphysics Workshop

Date: Monday, Nov 20, 4.15-6.15pm (NY time)

Room: Graduate Center Room 4419

Title: Truth with and without satisfaction

Abstract: The talk addresses a quite natural situation in mathematics. When one needs to define a concept and it is not possible to do a direct recursion on the concept itself, what one does is the next best thing which is to perform recursion on a related concept of which the original given concept can be shown to be a special case. Tarski, in his celebrated paper on “The Concept of Truth in Formalized Languages”, cannot give a definition of truth performing direct recursion on the concept of truth itself. Consequently, he settles on a definition in terms of satisfaction. Following Kit Fine and Timothy McCarthy, “Truth without Satisfaction”, I raise the issue of whether such an indirect procedure of giving a definition of truth is necessary or maybe an alternative definition of truth can be given without going through the related concept of satisfaction. My talk will investigate both certain technical and philosophical aspects of the two sets of formal constraints to defining truth with and without satisfaction.

- - - - Tuesday, Nov 28, 2023 - - - -

- - - - Wednesday, Nov 29, 2023 - - - -

The New York City Category Theory Seminar

Department of Computer Science

Department of Mathematics

The Graduate Center of The City University of New York

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

Date and Time: Wednesday November 29, 2023, 7:00 - 8:30 PM. ZOOM TALK.

- - - - Thursday, Nov 30, 2023 - - - -

- - - - Friday, Dec 1, 2023 - - - -

Rehana Patel Wesleyan University

CUNY Graduate Center

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@citytech.cuny.edu.

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

## Set Theory and Topology Seminar 21.11.2023 Diego Mejia

**Diego Mejia **(Shizuoka University)

Abstract.

About 15 minutes before the seminar we invite you for coffee and a chat to social room.

https://settheory.pwr.edu.pl/

http://www.math.uni.wroc.pl/seminarium/topologia

## Wednesday seminar

## (KGRC) two seminar talks Thursday, November 16

## This Week in Logic at CUNY

Rutgers Logic Seminar

Monday, Nov 13, 3:30pm, Rutgers University, Hill 705

Finite Tukey Morphisms

Date: Monday, Nov 13, 4.15-6.15pm (NY time)

Room: Graduate Center Room 4419

Alex Skiles (Rutgers).

Title: Against zero-grounding

Abstract: A number of philosophers believe that there is an intelligible distinction between ungrounded truths, which are not grounded in any truths at all, and zero-grounded truths, which are grounded, yet there are no truths that they are grounded in. Rather being a mere academic curiosity, these philosophers have also argued that the notion of zero-grounding can be put to serious metaphysical work. In this paper, we present two arguments against the intelligibility of zero-grounding, and then reject several attempts to make zero-grounding intelligible that have been suggested by its proponents.

Note: This is joint work with Tien-Chun Lo and Gonzalo Rodriguez-Pereyra.

- - - - Tuesday, Nov 14, 2023 - - - -

Models of Peano Arithmetic (MOPA)

Tuesday, Nov 14, 1:00pm

Virtual (email Victoria Gitman vgitman@gmail.com for meeting id)

On the (non)elementarity of cofinal extension

Compared with end extensions, much little is known about cofinal extensions for models of fragments of PA, especially their elementarity. In this talk, I will try to give a complete characterization of the elementarity of cofinal extensions. I will present a systematic way to `compress' the truth of M into the second-order structure of a definable cut, and as a consequence, a correspondence theorem between the first-order theory of M and the second-order theory of the cut. Through this method I will construct several models with special cofinal extension properties. I will also show that every countable model of arithmetic fail to satisfy PA admits a non-elementary cofinal extension. It provides a model-theoretic characterization for PA in terms of cofinal extensions.

- - - - Wednesday, Nov 15, 2023 - - - -

- - - - Thursday, Nov 16, 2023 - - - -

- - - - Friday, Nov 17, 2023 - - - -

Scott Mutchnik, University of Illinois at Chicago** Theories**

Among the classical properties of unstable theories defined by Shelah, our understanding of the strict order hierarchy, , has remained relatively limited past at the greatest. Methods originating from stability theory have given insight into the structure of stronger unstable classes, including simple and theories. In particular, syntactic information about formulas in a first-order theory often corresponds to semantic information about independence in a theory's models, which generalizes phenomena such as linear independence in vector spaces and algebraic independence in algebraically closed fields. We discuss how the fine structure of this independence reveals exponential behavior within the strict order hierarchy, particularly at the levels for positive integers . Our results suggest a potential theory of independence for theories, for arbitrarily large values of .

CUNY Graduate Center

**Joel David Hamkins**, Notre Dame University**The Wordle and Absurdle numbers**

We consider the game of infinite Wordle as played on Baire space . The codebreaker can win in finitely many moves against any countable dictionary , but not against the full dictionary of Baire space. The *Wordle number* is the size of the smallest dictionary admitting such a winning strategy for the codebreaker, the corresponding *Wordle ideal* is the ideal generated by these dictionaries, which under MA includes all dictionaries of size less than the continuum. The *Absurdle number*, meanwhile, is the size of the smallest dictionary admitting a winning strategy for the absurdist in the two-player variant, infinite Absurdle. In ZFC there are nondetermined Absurdle games, with neither player having a winning strategy, but if one drops the axiom of choice, then the principle of Absurdle determinacy has large cardinal consistency strength over ZF+DC. This is joint work with Ben De Bondt (Paris).

- - - - Monday, Nov 20, 2023 - - - -

Rutgers Logic Seminar

Monday, Nov 20, 3:30pm, Rutgers University, Hill 705

Logic and Metaphysics Workshop

Date: Monday, Nov 20, 4.15-6.15pm (NY time)

Room: Graduate Center Room 4419

Marian Călborean (Bucharest).

Title: Vagueness and Frege

Abstract: A constant of Frege’s writing is his rejection of indeterminate predicates in natural language. I follow Frege’s remarks on vagueness from the early “Begriffsschrift” to his mature works, drawing parallels with contemporary theories of vagueness. I critically examine Frege’s arguments for the inconsistency of natural language and argue that the inability to accommodate vagueness and precision in his mature ontology and semantics is mainly due to heuristic rules which he took as essential, not to a deep problem in his fundamental apparatus.

- - - - Tuesday, Nov 21, 2023 - - - -

Tuesday, Nov 21, 1:00pm

Virtual (email Victoria Gitman vgitman@gmail.com for meeting id)

- - - - Wednesday, Nov 22, 2023 - - - -

The New York City Category Theory Seminar

Department of Computer Science

Department of Mathematics

The Graduate Center of The City University of New York

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

**Pedro Sota, TBA.**

Date and Time:

**Wednesday November 22, 2023, 7:00 - 8:30 PM. ZOOM TALK.**

- - - - Thursday, Nov 23, 2023 - - - -

*** Graduate Center Closed (Thanksgiving) ***

- - - - Friday, Nov 24, 2023 - - - -

https://cims.nyu.edu/dynamic/conferences/davis-memorial/

The event plans presentations by Allyn Jackson, Eugenio Omodeo and Wilfried Sieg and a session on Memories of Martin and Virginia Davis.

People who cannot attend in person may submit a paragraph or two to the organizers to be read aloud at the event.

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@citytech.cuny.edu.

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

## Set Theory and Topology Seminar 14.11.2023 Aleksander Cieślak

| sob., 4 lis, 10:22 (8 dni temu) | |||

**Aleksander Cieślak**

Abstract.

About 15 minutes before the seminar we invite you for coffee and a chat to social room.

https://settheory.pwr.edu.pl/

http://www.math.uni.wroc.pl/seminarium/topologia

## Nankai Logic Colloquium

Hello everyone,

Welcome back to Nankai Logic Colloquium! This week our weekly Nankai Logic Colloquium is going to be in the morning.

Our speaker this week will be Marcin Sabok from McGill University. This talk is going to take place this Friday, Nov 17, from 9am to 10am(UTC+8, Beijing time).

___________________________________________________________________________________________________________________________________________________

Title ：The 34th Nankai Logic Colloquium --Marcin Sabok

Time ：9:00am, Nov. 17, 2023(Beijing Time)

Zoom Number ：872 7448 5609

Passcode ：448066

Link ：https://zoom.us/j/87274485609?pwd=z90Pn2KFasUa3KbbvQ1d7xSl3eP6rc.1

_____________________________________________________________________

Best wishes,

Ming Xiao

## (KGRC) two talks tomorrow, Thursday, November 9

## This Week in Logic at CUNY

Date: Monday, Nov 6, 4.15-6.15pm (NY time)

Room: Graduate Center Room 4419

Alex Citkin (Metropolitan Telecommunications).

Title: On logics of acceptance and rejection

Abstract: In his book *Formalization of Logic*, Carnap suggested the following process of refutation: for any set of formulas Γ and any formula *α,* if Γ ⊢ *α *and *α *is rejected, reject Γ. Thus, in contrast to the Łukasiewicz’s approach to refutation, the predicate of rejection is defined on sets of formulas rather than just formulas. In addition to a predicate of rejection, we introduce a predicate of acceptance which is also defined on sets of formulas, and this leads us to constructing two-layered logical systems, the ground layer of which is a conventional deductive system (providing us with means for derivation), and the top layer having predicates of acceptance and rejection. In the case when the set of accepted formulas coincides with the set of theorems of the underlying logic and the set of rejected formulas coincides with the sets of non-theorems, we obtain a conventional deductive system. The predicate of acceptance can be non-adjunctive, and this allows us to use such systems as an alternative approach to defining Jaśkowski style discursive logics.

- - - - Tuesday, Nov 7, 2023 - - - -

Models of Peano Arithmetic (MOPA)

Tuesday, Nov 7, 1:00pm

Virtual (email Victoria Gitman vgitman@gmail.com for meeting id)

This talk is about the relationship between (weak) arithmetical theories and methods for automated inductive theorem proving. Automating the search for proofs by induction is an important topic in computer science with a history that stretches back decades. A variety of different approaches, algorithms and implementations has been developed.

In this talk I will present a logical approach for understanding the power and limits of methods for automated inductive theorem proving. A central tool are translations of proof systems that are intended for automated proof search into weak arithmetical theories. Another central tool are non-standard models of these weak arithmetical theories.

This approach allows to obtain independence results which are of practical interest in computer science. It also gives rise to a number of new problems and questions about weak arithmetical theories.

- - - - Wednesday, Nov 8, 2023 - - - -

Philog Seminar

November 8, 2023, Wednesday, 10 AM

Zoom meeting, please contact Rohit Parikh for zoom link

Conversational strategy and political discourse

The New York City Category Theory Seminar

Department of Computer Science

Department of Mathematics

The Graduate Center of The City University of New York

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

Speaker: ** Larry Moss, Indiana University, Bloomington .**

Date and Time: ** Wednesday November 8, 2023, 7:00 - 8:30 PM. ZOOM TALK**

Title:** On Kripke, Vietoris, and Hausdorff Polynomial Functors.**

Abstract: The Vietoris space of compact subsets of a given Hausdorff space yields an endofunctor V on the category of Hausdorff spaces. Vietoris polynomial endofunctors on that category are built from V, the identity and constant functors by forming products, coproducts and compositions. These functors are known to have terminal coalgebras and we deduce that they also have initial algebras. We present an analogous class of endofunctors on the category of extended metric spaces, using in lieu of V the Hausdorff functor H. We prove that the ensuing Hausdorff polynomial functors have terminal coalgebras and initial algebras. Whereas the canonical constructions of terminal coalgebras for Vietoris polynomial functors takes omega steps, one needs \omega + \omega steps in general for Hausdorff ones. We also give a new proof that the closed set functor on metric spaces has no fixed points.

- - - - Thursday, Nov 9, 2023 - - - -

- - - - Friday, Nov 10, 2023 - - - -

**Asymptotics of the Spencer-Shelah Random Graph Sequence**

In combinatorics, the Spencer-Shelah random graph sequence is a variation on the independent-edge random graph model. We fix an irrational number , and we probabilistically generate the n-th Spencer-Shelah graph (with parameter ) by taking vertices, and for every pair of distinct vertices, deciding whether they are connected with a biased coin flip, with success probability . On the other hand, in model theory, an -mac is a class of finite structures, where the cardinalities of definable subsets are particularly well-behaved. In this talk, we will introduce the notion of 'probabalistic -mac' and present an incomplete proof that the Spencer Shelah random graph sequence is an example of one.

CUNY Graduate Center

**Victoria Gitman**, CUNY**Upward Löwenheim Skolem numbers for abstract logics**

Galeotti, Khomskii and Väänänen recently introduced the notion of the upward Löwenheim Skolem (ULS) number for an abstract logic. A cardinal is the upward Lowenheim Skolem number for a logic if it is the least cardinal with the property that whenever is a model of size at least satisfying a sentence in , then there are arbitrarily large models satisfying and having as a substructure (not necessarily elementary). If we remove the requirement that has to be a substructure of , we get the classic notion of a Hanf number. While proves that every logic has a Hanf number, having a ULS number often turns out to have large cardinal strength. In a joint work with Jonathan Osinski, we study the ULS numbers for several classical logics. We introduce a strengthening of the ULS number, the strong upward Löwenheim Skolem number SULS which strengthens the requirement that is a substructur