## 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**

(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

## 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 --------

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 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.

(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.

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.

(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.

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 --------

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.

## 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 substructure to full elementarity in the logic . It is easy to see that both the ULS and the SULS number for a logic are bounded by the least strong compactness cardinal for , if it exists.

- - - - Monday, Nov 13, 2023 - - - -

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 - - - -

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 7.11.2023 Zdenek Silber

**Zdenek Silber** (IM PAN)

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

## Set Theory and Topology Seminar 3.11.2023 Witold Marciszewski

**Friday 3.11.2023 at 16:15**in room 60x (Mathematical Institute, University of Wrocław) the lecture:

**Witold Marciszewski**(MIM UW)

Recall that a compact space K is Eberlein compact if it can be embedded into some Banach space X equipped with the weak topology; equivalently, for some set \Gamma, K can be embedded into the space c_0( \Gamma), endowed with the pointwise convergence topology.

A compact space K is \omega-Corson compact if, for some set \Gamma, K is homeomorphic to a subset of the \sigma-product of real lines \sigma(R^\Gamma), i.e. the subspace of the product R^\Gamma consisting of functions with finite supports. Clearly, every \omega-Corson compact space is Eberlein compact.

We will present a characterization of \omega-Corson compact spaces, and some other results concerning this class of spaces and related classes of Eberlein compacta.

This is a joint research with Grzegorz Plebanek and Krzysztof Zakrzewski, see

https://arxiv.org/abs/2107.02513

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

## Cross-Alps Logic Seminar (speaker: Steffen Lempp)

**Steffen Lempp**(University of Wisconsin)

will give a talk on

*The complexity of the class of models of arithmetic*Please refer to the usual webpage of our LogicGroup for more details and the abstract of the talk.

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

The Cross-Alps Logic Seminar is co-organized by the logic groups of Genoa, Lausanne, Turin and Udine as part of our collaboration in the project PRIN 2022 'Models, Sets and Classifications'.

## Cross-Alps Logic Seminar (speaker: Steffen Lempp)

**Steffen Lempp**(University of Wisconsin)

*The complexity of the class of models of arithmetic*

## This Week in Logic at CUNY

- - - - Monday, Oct 30, 2023 - - - -

Rutgers Logic Seminar

Monday, Oct 30th, 3:30pm, Rutgers University, Hill 705

Condensation and solvable left-orderable groups

Logic and Metaphysics Workshop

Date: Monday, Oct 30, 4.15-6.15pm (NY time)

Room: Graduate Center Room 4419

Title: An approach to property-talk for property nominalists

Abstract: Properties, understood as immanent universals that are repeatable entities which distinct objects can each have at the same time and in different places, are weird, so weird, in fact, that if we could do without them, we probably should do so. An alternative to an approach that sanctions properties might suggest a deflationary view of property-talk according to which the raison d’être of our use of ‘property’ is that it serves a quasi-logical function that is akin to what alethic deflationists claim about truth-talk. Deflationists about property-talk normally subscribe to a form of property nominalism, which rejects the sort of property realism that takes properties to be immanent universals. In this talk, after highlighting some of the weirdness of, or worries for, property realism and explaining why certain forms of property nominalism should not be abided, I highlight the expressive role of property-talk and go on to explain how property-talk performs its roles by introducing what I call “adjectival predicate-variable deflationism” (“APVD”). As I will show, by incorporating APVD into a version of what I have called a “semantic-pretense involving fictionalism” (“SPIF”), we capture the full range of property-talk instances without compromising property nominalism. Time permitting, I will also highlight a virtue of my view, which another form of property nominalism cannot accommodate. If property nominalism is correct, then we should endorse the SPIF account of property-talk that I will develop in this talk.

Note: This is joint work with James A. Woodbridge.

- - - - Tuesday, Oct 31, 2023 - - - -

- - - - Wednesday, Nov 1, 2023 - - - -

- - - - Thursday, Nov 2, 2023 - - - -

- - - - Friday, Nov 3, 2023 - - - -

CUNY Graduate Center

Nonstandard methods without the Axiom of Choice

Mikhail Katz and I have formulated a set theory SPOT in the language that has, in addition to membership, a unary predicate “is standard.” In addition to ZF, the theory has 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 as far as the global version of Peano's Theorem (the usual proofs of which use ADC, the Axiom of Dependent Choice). The existence of upper Banach densities can be proved in SPOT.

The conservativity of SPOT over ZF is established by a construction that combines the methods of forcing developed by Ali Enayat for second-order arithmetic and Mitchell Spector for set theory with large cardinals.

A stronger theory SCOT is a conservative extension of ZF+ADC. It is suitable for handling such features as an infinitesimal approach to the Lebesgue measure.

I will also formulate an extension of SPOT to a theory with multiple levels of standardness SPOTS, in which Renling Jin's recent groundbreaking proof of Szemeredi's Theorem can be carried out. While it is an open question whether SPOTS is conservative over ZF, SPOTS + DC (Dependent Choice for relations definable in it) is a conservative extension of ZF + ADC.

Reference: KH and M. G. Katz, Infinitesimal analysis without the Axiom of Choice, Ann. Pure Applied Logic 172, 6 (2021). https://doi.org/10.1016/j.apal.2021.102959, https://arxiv.org/abs/2009.04980

- - - - Monday, Nov 6, 2023 - - - -

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)

- - - - Wednesday, Nov 8, 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

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 - - - -

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 substructure to full elementarity in the logic . It is easy to see that both the ULS and the SULS number for a logic are bounded by the least strong compactness cardinal for , if it exists.

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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## Set Theory and Topology Seminar 31.10.2023 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

## Wednesday seminar

## This Week in Logic at CUNY

Rutgers Logic Seminar

Monday, Oct 23rd, 3:30pm, Rutgers University, Hill 705

Logic and Metaphysics Workshop

Date: Monday, Oct 23, 4.15-6.15pm (NY time)

Melissa Fusco (Columbia)

Title: Diachronic reasoning with conditionals

Abstract: I will discuss a hybrid decision theory, coinciding sometimes with (traditional) Evidential Decision Theory, but usually with (traditional) Causal Decision Theory, which is inspired by recent work on unified and fully compositional approaches to the probabilities of conditionals. The hybrid theory features a few other loci of interest: the partitionality of acts A ∈ {A} fails, and close attention is paid to how one might (dis)confirm chance hypotheses under the umbrella of the Principal Principle. On this theory, the probabilities of conditionals play a role in underwriting a theory of imaging that follows Skyrms’s Thesis (Skyrms, 1981, 1984). Moreover, the credences it is epistemically rational to assign to these conditionals guides updating on one’s own acts. This implies some departures from Conditionalization, which I defend on epistemological grounds.

- - - - Tuesday, Oct 24, 2023 - - - -

Models of Peano Arithmetic (MOPA)

Tuesday, Oct 24, 1:00pm

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

Alessandro Berarducci and Marcello Mamino, University of Pisa**Provability logic: models within models in Peano Arithmetic**

In 1994 Jech gave a model theoretic proof of Gödel's second incompleteness theorem for Zermelo-Fraenkel set theory in the following form: ZF does not prove that ZF has a model. Kotlarski showed that Jech's proof can be adapted to Peano Arithmetic with the role of models being taken by complete consistent extensions. In this note we take another step in the direction of replacing proof-theoretic by model-theoretic arguments. We show, without passing through the arithmetized completeness theorem, that the existence of a model of PA of complexity is independent of PA, where a model is identified with the set of formulas with parameters which hold in the model. Our approach is based on a new interpretation of the provability logic of Peano Arithmetic with the modal operator interpreted as truth in every -model.

- - - - Wednesday, Oct 25, 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

Speaker: ** Emilio Minichiello, CUNY Graduate Center.**

Date and Time: ** Wednesday October 25, 2023, 7:00 - 8:30 PM. IN PERSON TALK (GC 6417)**

Title:** A Mathematical Model of Package Management Systems.**

Abstract: In this talk, I will review some recent joint work with Gershom Bazerman and Raymond Puzio. The motivation is simple: provide a mathematical model of package management systems, such as the Hackage package respository for Haskell, or Homebrew for Mac users. We introduce Dependency Structures with Choice (DSC) which are sets equipped with a collection of possible dependency sets for every element and satisfying some simple conditions motivated from real life use cases. We define a notion of morphism of DSCs, and prove that the resulting category of DSCs is equivalent to the category of antimatroids, which are mathematical structures found in combinatorics and computer science. We analyze this category, proving that it is finitely complete, has coproducts and an initial object, but does not have all coequalizers. Further, we construct a functor from a category of DSCs equipped with a certain subclass of morphisms to the opposite of the category of finite distributive lattices, making use of a simple finite characterization of the Bruns-Lakser completion.

- - - - Thursday, Oct 26, 2023 - - - -

- - - - Friday, Oct 27, 2023 - - - -

CUNY Graduate Center

**Arnon Avron**, Tel Aviv University**Poincaré-Weyl's predicativity: going beyond **

On the basis of Poincaré and Weyl's view of predicativity as invariance, we develop an extensive framework for predicative, type-free first-order set theory in which and much bigger ordinals can be defined as von Neumann ordinals. This refutes the accepted view of as the 'limit of predicativity.' We also explain what is wrong in Feferman-Schütte analysis of predicativity on which this view of is based.

- - - - Monday, Oct 30, 2023 - - - -

Rutgers Logic Seminar

Monday, Oct 30th, 3:30pm, Rutgers University, Hill 705

Logic and Metaphysics Workshop

Date: Monday, Oct 30, 4.15-6.15pm (NY time)

Room: Graduate Center Room 4419

Title: An approach to property-talk for property nominalists

Abstract: Properties, understood as immanent universals that are repeatable entities which distinct objects can each have at the same time and in different places, are weird, so weird, in fact, that if we could do without them, we probably should do so. An alternative to an approach that sanctions properties might suggest a deflationary view of property-talk according to which the raison d’être of our use of ‘property’ is that it serves a quasi-logical function that is akin to what alethic deflationists claim about truth-talk. Deflationists about property-talk normally subscribe to a form of property nominalism, which rejects the sort of property realism that takes properties to be immanent universals. In this talk, after highlighting some of the weirdness of, or worries for, property realism and explaining why certain forms of property nominalism should not be abided, I highlight the expressive role of property-talk and go on to explain how property-talk performs its roles by introducing what I call “adjectival predicate-variable deflationism” (“APVD”). As I will show, by incorporating APVD into a version of what I have called a “semantic-pretense involving fictionalism” (“SPIF”), we capture the full range of property-talk instances without compromising property nominalism. Time permitting, I will also highlight a virtue of my view, which another form of property nominalism cannot accommodate. If property nominalism is correct, then we should endorse the SPIF account of property-talk that I will develop in this talk.

Note: This is joint work with James A. Woodbridge.

- - - - Tuesday, Oct 31, 2023 - - - -

- - - - Wednesday, Nov 1, 2023 - - - -

- - - - Thursday, Nov 2, 2023 - - - -

- - - - Friday, Nov 3, 2023 - - - -

CUNY Graduate Center

Nonstandard methods without the Axiom of Choice

Mikhail Katz and I have formulated a set theory SPOT in the language that has, in addition to membership, a unary predicate “is standard.” In addition to ZF, the theory has 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 as far as the global version of Peano's Theorem (the usual proofs of which use ADC, the Axiom of Dependent Choice). The existence of upper Banach densities can be proved in SPOT.

The conservativity of SPOT over ZF is established by a construction that combines the methods of forcing developed by Ali Enayat for second-order arithmetic and Mitchell Spector for set theory with large cardinals.

A stronger theory SCOT is a conservative extension of ZF+ADC. It is suitable for handling such features as an infinitesimal approach to the Lebesgue measure.

I will also formulate an extension of SPOT to a theory with multiple levels of standardness SPOTS, in which Renling Jin's recent groundbreaking proof of Szemeredi's Theorem can be carried out. While it is an open question whether SPOTS is conservative over ZF, SPOTS + DC (Dependent Choice for relations definable in it) is a conservative extension of ZF + ADC.

Reference: KH and M. G. Katz, Infinitesimal analysis without the Axiom of Choice, Ann. Pure Applied Logic 172, 6 (2021). https://doi.org/10.1016/j.apal.2021.102959, https://arxiv.org/abs/2009.04980

The 2023 Category Theory Octoberfest will be held on the weekend of October 28th through October 29th. The meeting will be virtual. Following the tradition of past Octoberfests, this is intended to be an informal meeting, covering all areas of category theory and its applications. Here is the official conference website:

https://richardblute.ca/octoberfest-2023/

At the moment, you'll find there the schedule with all speakers and titles, as well as the zoom link which will be the same for both days. The abstracts for all the talks will be available shortly.

- - - - Web Site - - - -

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

(site designed, built & maintained by Victoria Gitman)

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

To subscribe/unsubscribe to this list, please email your request to jreitz@citytech.cuny.edu.

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

## Logic Seminar Talks at NUS on 24 Oct, 31 Oct and 7 Nov 2023

## (KGRC) talk in the Model Theory Seminar on Wednesday, October 25

## Set Theory and Topology Seminar 24.10.2023 Maciej Korpalski

**Maciej Korpalski**

**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

## (KGRC) seminar talks Wednesday, October 18, and Thursday, October 19

## This Week in Logic at CUNY

Monday, Oct 16th, 3:30pm, Rutgers University, Hill 705

Large minimal non-σ-scattered linear orders

Logic and Metaphysics Workshop

Date: Monday, Oct 16, 4.15-6.15pm (NY time)

Title: Maximal deontic logic

Abstract: The worlds accessible from a given world in Kripke models for deontic logic are often informally glossed as ideal or perfect worlds (at least, relative to the base world). Taking that language seriously, a straightforward but nonstandard semantic implementation using models containing maximally good worlds yields a deontic logic, MD, considerably stronger than that which most logicians would advocate for. In this talk, I examine this logic, its philosophical significance, and its technical properties, as well as those of the logics in its vicinity. The principal technical result is a proof that MD is pretabular (it has no finite characteristic matrix but all of its proper normal extensions do). Along the way, I also characterize all normal extensions of the quirky deontic logic D4H, prove that they are all decidable, and show that D4H has exactly two pretabular normal extensions.

- - - - Tuesday, Oct 17, 2023 - - - -

Models of Peano Arithmetic (MOPA)

Tuesday, Oct 17, 1:00pm

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

Elliot Glazer, Harvard University**Coin flipping on models of arithmetic to define the standard cut**

We will discuss the following claim: 'The standard cut of a model of PA (or even Q) is uniformly definable with respect to a randomly chosen predicate.' Restricting our consideration to countable models, this claim is true in the usual sense, i.e. there is a formula such that for any countable model of arithmetic the set is Lebesgue measure 1. However, if is countably saturated, then there is no such that is measured by the completed product measure on We will identify various combinatorial ideals on that can be used to formalize the original claim with no restriction on the cardinality of and discuss the relationship between closure properties of these ideals and principles of choice.

- - - - Wednesday, Oct 18, 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

Speaker: ** Michael Shulman, University of San Diego.**

Date and Time: ** Wednesday October 18, 2023, 7:00 - 8:30 PM. ZOOM TALK**

Title:** The derivator of setoids.**

Abstract: The question of "what is a homotopy theory" or "what is a higher category" is already interesting in classical mathematics, but in constructive mathematics (such as the internal logic of a topos) it becomes even more subtle. In particular, existing constructive attempts to formulate a homotopy theory of spaces (infinity-groupoids) have the curious property that their "0-truncated objects" are more general than ordinary sets, being instead some kind of "free exact completion" of the category of sets (a.k.a. "setoids"). It is at present unclear whether this is a necessary feature of a constructive homotopy theory or whether it can be avoided somehow. One way to find some evidence about this question is to use the "derivators" of Heller, Franke, and Grothendieck, as they give us access to higher homotopical structure without depending on a preconcieved notion of what such a thing should be. It turns out that constructively, the free exact completion of the category of sets naturally forms a derivator that has a universal property analogous to the classical category of sets and to the classical homotopy theory of spaces: it is the "free cocompletion of a point" in a certain universe. This suggests that either setoids are an unavoidable aspect of constructive homotopy theory, or more radical modifications to the notion of homotopy theory are needed.

- - - - Thursday, Oct 19, 2023 - - - -

- - - - Friday, Oct 20, 2023 - - - -

CUNY Graduate Center

**The number of ergodic models of an infinitary sentence**

Given an -sentence in a countable language, we call an ergodic -invariant probability measure on the Borel space of countable models of (having fixed underlying set) an *ergodic model* of . I will discuss the number of ergodic models of such a sentence , including the case when is a Scott sentence. This is joint work with N. Ackerman, C. Freer, A. Kruckman and A. Kwiatkowska.

- - - - Monday, Oct 23, 2023 - - - -

Rutgers Logic Seminar

Monday, Oct 23rd, 3:30pm, Rutgers University, Hill 705

Logic and Metaphysics Workshop

Date: Monday, Oct 23, 4.15-6.15pm (NY time)

Melissa Fusco (Columbia)

Title: Diachronic reasoning with conditionals

Abstract: I will discuss a hybrid decision theory, coinciding sometimes with (traditional) Evidential Decision Theory, but usually with (traditional) Causal Decision Theory, which is inspired by recent work on unified and fully compositional approaches to the probabilities of conditionals. The hybrid theory features a few other loci of interest: the partitionality of acts A ∈ {A} fails, and close attention is paid to how one might (dis)confirm chance hypotheses under the umbrella of the Principal Principle. On this theory, the probabilities of conditionals play a role in underwriting a theory of imaging that follows Skyrms’s Thesis (Skyrms, 1981, 1984). Moreover, the credences it is epistemically rational to assign to these conditionals guides updating on one’s own acts. This implies some departures from Conditionalization, which I defend on epistemological grounds.

- - - - Tuesday, Oct 24, 2023 - - - -

Models of Peano Arithmetic (MOPA)

Tuesday, Oct 24, 1:00pm

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

Alessandro Berarducci and Marcello Mamino, University of Pisa**Provability logic: models within models in Peano Arithmetic**

In 1994 Jech gave a model theoretic proof of Gödel's second incompleteness theorem for Zermelo-Fraenkel set theory in the following form: ZF does not prove that ZF has a model. Kotlarski showed that Jech's proof can be adapted to Peano Arithmetic with the role of models being taken by complete consistent extensions. In this note we take another step in the direction of replacing proof-theoretic by model-theoretic arguments. We show, without passing through the arithmetized completeness theorem, that the existence of a model of PA of complexity is independent of PA, where a model is identified with the set of formulas with parameters which hold in the model. Our approach is based on a new interpretation of the provability logic of Peano Arithmetic with the modal operator interpreted as truth in every -model.

- - - - Wednesday, Oct 25, 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

Speaker: ** Emilio Minichiello, CUNY Graduate Center.**

Date and Time: ** Wednesday October 25, 2023, 7:00 - 8:30 PM. IN PERSON TALK (GC 6417)**

Title:** A Mathematical Model of Package Management Systems.**

Abstract: In this talk, I will review some recent joint work with Gershom Bazerman and Raymond Puzio. The motivation is simple: provide a mathematical model of package management systems, such as the Hackage package respository for Haskell, or Homebrew for Mac users. We introduce Dependency Structures with Choice (DSC) which are sets equipped with a collection of possible dependency sets for every element and satisfying some simple conditions motivated from real life use cases. We define a notion of morphism of DSCs, and prove that the resulting category of DSCs is equivalent to the category of antimatroids, which are mathematical structures found in combinatorics and computer science. We analyze this category, proving that it is finitely complete, has coproducts and an initial object, but does not have all coequalizers. Further, we construct a functor from a category of DSCs equipped with a certain subclass of morphisms to the opposite of the category of finite distributive lattices, making use of a simple finite characterization of the Bruns-Lakser completion.

- - - - Thursday, Oct 26, 2023 - - - -

- - - - Friday, Oct 27, 2023 - - - -

CUNY Graduate Center

**Arnon Avron**, Tel Aviv University**Poincaré-Weyl's predicativity: going beyond **

On the basis of Poincaré and Weyl's view of predicativity as invariance, we develop an extensive framework for predicative, type-free first-order set theory in which and much bigger ordinals can be defined as von Neumann ordinals. This refutes the accepted view of as the 'limit of predicativity.' We also explain what is wrong in Feferman-Schütte analysis of predicativity on which this view of is based.

Place: Wellesley College – All talks in Science Center N321

Gihanee Senadheera (Winthrop College)

Alex van Abel (Wesleyan University)

Neil Lutz (Swarthmore College)

Please find the webpage containing all relevant information below. Registration is optional but strongly encouraged for planning purpose.

https://sites.math.rutgers.edu/~fc327/GLaDF2023/index.html

- - - - Web Site - - - -

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

(site designed, built & maintained by Victoria Gitman)

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

To subscribe/unsubscribe to this list, please email your request to jreitz@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 17.10.2023 Viktoriia Brydun

**Viktoriia Brydun **(Ivan Franko Lviv National University)

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

## Logic Seminar 17 Oct 2023 17:00 hrs by Frank Stephan at NUS Mathematics

## (KGRC) talks Wednesday (TODAY), Thursday, and Friday

## This Week in Logic at CUNY

CUNY Graduate Center CLOSED TODAY

- - - - Tuesday, Oct 10, 2023 - - - -

- - - - Wednesday, Oct 11, 2023 - - - -

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: ** Thiago Alexandre, University of São Paulo (Brazil).**

Date and Time: ** Wednesday October 11, 2023, 7:00 - 8:30 PM.**

Title:** Internal homotopy theories.**

Abstract: The idea of 'Homotopy theories' was introduced by Heller in his seminal paper from 1988. Two years later, Grothendieck discovered the theory of derivators (1990), exposed in his late manuscript Les Dérivateurs, and developed further by several authors. Essentially, there are no significant differences between Heller's homotopy theories and Grothendieck's derivators. They are tautologically the same 2-categorical yoga. However, they come from distinct motivations. For Heller, derivators should be a definitive answer to the question "What is a homotopy theory?", while for Grothendieck, who was strongly inspired by topos cohomology, the first main motivation for derivators was to surpass some technical deficiencies that appeared in the theory of triangulated categories. Indeed, Grothendieck designed the axioms of derivators in light of a certain 2-functorial construction, which associates the corresponding (abelian) derived category to each topos, and more importantly, inverse and direct cohomological images to each geometric morphism. It was from this 2-functorial construction, from where topos cohomology arises, that Grothendieck discovered the axioms of derivators, which are surprisingly the same as Heller's homotopy theories. Nowadays, it is commonly accepted that a homotopy theory is a quasi-category, and they can all be presented by a localizer (M,W), i.e., a couple composed by a category M and a class of arrows in W. This point of view is not so far from Heller, since pre-derivators, quasi-categories, and localizers, are essentially equivalent as an answer to the question "What is a homotopy theory?". In my talk, I will expose these subjects in more detail, and I am also going to explore how to internalize a homotopy theory in an arbitrary (Grothendieck) topos, a problem which strongly relates formal logic and homotopical algebra.

- - - - Thursday, Oct 12, 2023 - - - -

- - - - Friday, Oct 13, 2023 - - - -

**Vincent Guingona**, Towson University**Indivisibility of Classes of Graphs**

This talk will discuss my work with Miriam Parnes and four undergraduates which took place last summer at an REU at Towson University. We say that a class of structures in some fixed language is indivisible if, for all structures A in the class and number of colors k, there is a structure B in the class such that, no matter how we color B with k colors, there is a monochromatic copy of A in B. Parnes and I became interested in this property when studying the classification of theories via positive combinatorial configurations. In this talk, following the work with our students, I will examine indivisibility on classes of graphs. In particular, we will look at hereditarily sparse graphs, cographs, perfect graphs, threshold graphs, and a few other classes. *This work is joint with Felix Nusbaum, Zain Padamsee, Miriam Parnes, Christian Pippin, and Ava Zinman*.

CUNY Graduate Center

Philipp Rothmaler, CUNY**A theorem of Makkai implying the existence of strict Mittag-Leffler modules in a definable subcategory**

In 1982 Makkai published a very general theorem about the existence of what he later called principally prime (we call them positive atomic) models of so-called regular theories [FULL CONTINUOUS EMBEDDINGS OF TOPOSES, TAMS 269], which seems to have gone largely unnoticed. (Regular he called those theories that are axiomatized by positive primitive (=pp) implications.) This is a strong existence result in some sort of positive logic in a very general categorical (including non-additive) setting. I first discuss its significance for definable subcategories of modules (=model categories of regular theories of modules), which play an important role in representation theory and module theory in general. Part of this is that there these models are precisely the strict Mittag-Leffler modules contained in and relativized to such definable subcategories. Makkai’s original proof is, in its generality, not easy to follow, and so it is of interest, especially to the algebraic community, to find an easier proof for modules. I present a recent one due to Prest. At the time being it works only for countable rings, in the uncountable case one still has to rely on Makkai’s original proof.

Place: Wellesley College – All talks in Science Center N321

- - - - Monday, Oct 16, 2023 - - - -

Monday, Oct 16th, 3:30pm, Rutgers University, Hill 705

Large minimal non-σ-scattered linear orders

Logic and Metaphysics Workshop

Date: Monday, Oct 16, 4.15-6.15pm (NY time)

Title: Maximal deontic logic

Abstract: The worlds accessible from a given world in Kripke models for deontic logic are often informally glossed as ideal or perfect worlds (at least, relative to the base world). Taking that language seriously, a straightforward but nonstandard semantic implementation using models containing maximally good worlds yields a deontic logic, MD, considerably stronger than that which most logicians would advocate for. In this talk, I examine this logic, its philosophical significance, and its technical properties, as well as those of the logics in its vicinity. The principal technical result is a proof that MD is pretabular (it has no finite characteristic matrix but all of its proper normal extensions do). Along the way, I also characterize all normal extensions of the quirky deontic logic D4H, prove that they are all decidable, and show that D4H has exactly two pretabular normal extensions.

- - - - Tuesday, Oct 17, 2023 - - - -

Models of Peano Arithmetic (MOPA)

Tuesday, Oct 17, 1:00pm

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

Elliot Glazer, Harvard University**Coin flipping on models of arithmetic to define the standard cut**

We will discuss the following claim: 'The standard cut of a model of PA (or even Q) is uniformly definable with respect to a randomly chosen predicate.' Restricting our consideration to countable models, this claim is true in the usual sense, i.e. there is a formula such that for any countable model of arithmetic the set is Lebesgue measure 1. However, if is countably saturated, then there is no such that is measured by the completed product measure on We will identify various combinatorial ideals on that can be used to formalize the original claim with no restriction on the cardinality of and discuss the relationship between closure properties of these ideals and principles of choice.

- - - - Wednesday, Oct 18, 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

Speaker: ** Michael Shulman, University of San Diego.**

Date and Time: ** Wednesday October 18, 2023, 7:00 - 8:30 PM.**

Title:** The derivator of setoids.**

- - - - Thursday, Oct 19, 2023 - - - -

- - - - Friday, Oct 20, 2023 - - - -

CUNY Graduate Center

Place: Wellesley College – All talks in Science Center N321

Gihanee Senadheera (Winthrop College)

Alex van Abel (Wesleyan University)

Neil Lutz (Swarthmore College)

Please find the webpage containing all relevant information below. Registration is optional but strongly encouraged for planning purpose.

https://sites.math.rutgers.edu/~fc327/GLaDF2023/index.html

- - - - Web Site - - - -

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

(site designed, built & maintained by Victoria Gitman)

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

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

## Set Theory and Topology Seminar 10.10.2023 Arturo Martinez

**603**(

**Mathematical Institute**,

**University of**

**Wrocław**) the lecture:

**Arturo Martinez**

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

## This Week in Logic at CUNY

- - - - Monday, Oct 2, 2023 - - - -

Rutgers Logic Seminar

Monday, Oct 2nd, 3:30pm, Rutgers University, Hill 705

Characterizing LEF groups

Abstract: We propose a concrete characterization of locally-embeddable-into-finite (LEF) groups of cardinality larger than the continuum in terms of embeddings into the reduced product of finite symmetric groups. We show that whether this characterization holds is independent of ZFC. Analogous work has been done for the more general class of sofic groups. This is joint work with Simon Thomas.

Logic and Metaphysics Workshop

Date: Monday, Oct 2, 4.15-6.15pm (NY time)

Title: Whence admissibility constraints? From inferentialism to tolerance

Abstract: Prior’s invented connective ‘tonk’ is sometimes taken to reveal a problem for certain inferentialist approaches to metasemantics: according to such approaches, the truth-theoretic features of our expressions are fully determined by the rules of inference we’re disposed to follow, but admitting the ‘tonk’ rules into a language would lead to intuitively absurd results. Inferentialists tend to insist that they can avoid these results: there are constraints on what sets of inference rules can be admitted into a language, the story goes, and the rules governing disruptive expressions like ‘tonk’ are defective and so illegitimate. I argue, though, that from an inferentialist perspective, there’s no genuine sense in which rules like the ‘tonk’ rules are defective; those who endorse the relevant sort of inferentialism turn out to be committed to Carnap’s principle of tolerance. I then sketch an argument to the effect that this, despite appearances, isn’t a problem for inferentialism.

- - - - Tuesday, Oct 3, 2023 - - - -

- - - - Wednesday, Oct 4, 2023 - - - -

- - - - Thursday, Oct 5, 2023 - - - -

- - - - Friday, Oct 6, 2023 - - - -

CUNY Graduate Center

Jenna Zomback, University of Maryland**Ergodic theorems along trees**

In the classical pointwise ergodic theorem for a probability measure preserving (pmp) transformation , one takes averages of a given integrable function over the intervals in front of the point . We prove a “backward” ergodic theorem for a countable-to-one pmp , where the averages are taken over subtrees of the graph of that are rooted at and lie behind (in the direction of ). Surprisingly, this theorem yields forward ergodic theorems for countable groups, in particular, one for pmp actions of free groups of finite rank, and can be extended to yield ergodic theorems for pmp actions of free semigroups as well. In each case, the averages are taken along subtrees of the standard Cayley graph rooted at the identity. This is joint work with Anush Tserunyan.

- - - - Monday, Oct 9, 2023 - - - -

- - - - Tuesday, Oct 10, 2023 - - - -

- - - - Wednesday, Oct 11, 2023 - - - -

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

**Thiago Alexandre,**

**Wednesday October 11, 2023, 7:00 - 8:30 PM.**

**...derivator....**

- - - - Thursday, Oct 12, 2023 - - - -

- - - - Friday, Oct 13, 2023 - - - -

Please find the webpage containing all relevant information below. Registration is optional but strongly encouraged for planning purpose.

https://sites.math.rutgers.edu/~fc327/GLaDF2023/index.html

- - - - Web Site - - - -

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

(site designed, built & maintained by Victoria Gitman)

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

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

## Update - Logic Workshop cancelled today: This Week in Logic at CUNY

**James Walsh**in the Logic Workshop is cancelled due to flooding and subway outages. Everyone be careful out there,

- - - - Monday, Sep 25, 2023 - - - -

NO CLASSES AT CUNY TODAY

Monday, Sept 25th, 3:30pm, Rutgers University, Hill 705

Mutual stationarity and the failure of SCH

- - - - Tuesday, Sep 26, 2023 - - - -

- - - - Wednesday, Sep 27, 2023 - - - -

This Week in Logic at CUNY:

- - - - Monday, Sep 25, 2023 - - - -

NO CLASSES AT CUNY TODAYRutgers Logic Seminar

Monday, Sept 25th, 3:30pm, Rutgers University, Hill 705Dima Sinapova, Rutgers

Mutual stationarity and the failure of SCH

- - - - Tuesday, Sep 26, 2023 - - - -

- - - - Wednesday, Sep 27, 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.htmlSpeaker:Tomáš Gonda, University of Innsbruck.Date and Time:Wednesday September 27, 2023, 5:00 - 6:00 PM. ZOOM TALK. NOTE SPECIAL TIME!Title:A Framework for Universality in Physics, Computer Science, and Beyond.Abstract: Turing machines and spin models share a notion of universality according to which some simulate all others. We set up a categorical framework for universality which includes as instances universal Turing machines, universal spin models, NP completeness, top of a preorder, denseness of a subset, and others. By identifying necessary conditions for universality, we show that universal spin models cannot be finite. We also characterize when universality can be distinguished from a trivial one and use it to show that universal Turing machines are non-trivial in this sense. We leverage a Fixed Point Theorem inspired by a result of Lawvere to establish that universality and negation give rise to unreachability (such as uncomputability). As such, this work sets the basis for a unified approach to universality and invites the study of further examples within the framework.

- - - - Thursday, Sep 28, 2023 - - - -

- - - - Friday, Sep 29, 2023 - - - -Logic Workshop

CUNY Graduate CenterFriday Sept 29, 2:00pm-3:30pm, Room 6417

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.

Next Week in Logic at CUNY:

- - - - Monday, Oct 2, 2023 - - - -

Rutgers Logic Seminar

Monday, Oct 2nd, 3:30pm, Rutgers University, Hill 705Philip Stetson, Rutgers

Characterizing LEF groups

Logic and Metaphysics Workshop

Date: Monday, Oct 2, 4.15-6.15pm (NY time)Room: Graduate Center Room 4419For meeting information, please sign up for our mailing list at https://logic.commons.gc.cuny.edu/about/Brett Topey (Salzburg)

Title: Whence admissibility constraints? From inferentialism to tolerance

Abstract: Prior’s invented connective ‘tonk’ is sometimes taken to reveal a problem for certain inferentialist approaches to metasemantics: according to such approaches, the truth-theoretic features of our expressions are fully determined by the rules of inference we’re disposed to follow, but admitting the ‘tonk’ rules into a language would lead to intuitively absurd results. Inferentialists tend to insist that they can avoid these results: there are constraints on what sets of inference rules can be admitted into a language, the story goes, and the rules governing disruptive expressions like ‘tonk’ are defective and so illegitimate. I argue, though, that from an inferentialist perspective, there’s no genuine sense in which rules like the ‘tonk’ rules are defective; those who endorse the relevant sort of inferentialism turn out to be committed to Carnap’s principle of tolerance. I then sketch an argument to the effect that this, despite appearances, isn’t a problem for inferentialism.

- - - - Tuesday, Oct 3, 2023 - - - -

- - - - Wednesday, Oct 4, 2023 - - - -

- - - - Thursday, Oct 5, 2023 - - - -

- - - - Friday, Oct 6, 2023 - - - -Logic Workshop

CUNY Graduate CenterFriday Sept 29, 2:00pm-3:30pm, Room 6417Jenna Zomback, University of Maryland

Ergodic theorems along treesIn the classical pointwise ergodic theorem for a probability measure preserving (pmp) transformation , one takes averages of a given integrable function over the intervals in front of the point . We prove a “backward” ergodic theorem for a countable-to-one pmp , where the averages are taken over subtrees of the graph of that are rooted at and lie behind (in the direction of ). Surprisingly, this theorem yields forward ergodic theorems for countable groups, in particular, one for pmp actions of free groups of finite rank, and can be extended to yield ergodic theorems for pmp actions of free semigroups as well. In each case, the averages are taken along subtrees of the standard Cayley graph rooted at the identity. This is joint work with Anush Tserunyan.

- - - - Other Logic News - - - -CONFERENCE ANNOUNCEMENTI am glad to announce the first installment of the meeting Groups Logic and Dynamics, on October 21. This will be a one day meeting held in New Brunswick. The format is modelled after the NERDS (https://nerds.math.uconn.edu/), for those of you who are familiar with it.

Please find the webpage containing all relevant information below. Registration is optional but strongly encouraged for planning purpose.

https://sites.math.rutgers.edu/~fc327/GLaDF2023/index.html- Filippo Calderonifc327 (at) math.rutgers.edu

- - - - Web Site - - - -

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

(site designed, built & maintained by Victoria Gitman)

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

To subscribe/unsubscribe to this list, please email your request to jreitz@citytech.cuny.edu.

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

## This Week in Logic at CUNY

- - - - Monday, Sep 25, 2023 - - - -

NO CLASSES AT CUNY TODAY

Monday, Sept 25th, 3:30pm, Rutgers University, Hill 705

Mutual stationarity and the failure of SCH

- - - - Tuesday, Sep 26, 2023 - - - -

- - - - Wednesday, Sep 27, 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

**Tomáš Gonda, University of Innsbruck.**

**Wednesday September 27, 2023, 5:00 - 6:00 PM. ZOOM TALK. NOTE SPECIAL TIME!**

**A Framework for Universality in Physics, Computer Science, and Beyond.**

- - - - Thursday, Sep 28, 2023 - - - -

- - - - Friday, Sep 29, 2023 - - - -

CUNY Graduate Center

**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, Oct 2, 2023 - - - -

Rutgers Logic Seminar

Monday, Oct 2nd, 3:30pm, Rutgers University, Hill 705

Characterizing LEF groups

Logic and Metaphysics Workshop

Date: Monday, Oct 2, 4.15-6.15pm (NY time)

Title: Whence admissibility constraints? From inferentialism to tolerance

Abstract: Prior’s invented connective ‘tonk’ is sometimes taken to reveal a problem for certain inferentialist approaches to metasemantics: according to such approaches, the truth-theoretic features of our expressions are fully determined by the rules of inference we’re disposed to follow, but admitting the ‘tonk’ rules into a language would lead to intuitively absurd results. Inferentialists tend to insist that they can avoid these results: there are constraints on what sets of inference rules can be admitted into a language, the story goes, and the rules governing disruptive expressions like ‘tonk’ are defective and so illegitimate. I argue, though, that from an inferentialist perspective, there’s no genuine sense in which rules like the ‘tonk’ rules are defective; those who endorse the relevant sort of inferentialism turn out to be committed to Carnap’s principle of tolerance. I then sketch an argument to the effect that this, despite appearances, isn’t a problem for inferentialism.

- - - - Tuesday, Oct 3, 2023 - - - -

- - - - Wednesday, Oct 4, 2023 - - - -

- - - - Thursday, Oct 5, 2023 - - - -

- - - - Friday, Oct 6, 2023 - - - -

CUNY Graduate Center

Jenna Zomback, University of Maryland**Ergodic theorems along trees**

In the classical pointwise ergodic theorem for a probability measure preserving (pmp) transformation , one takes averages of a given integrable function over the intervals in front of the point . We prove a “backward” ergodic theorem for a countable-to-one pmp , where the averages are taken over subtrees of the graph of that are rooted at and lie behind (in the direction of ). Surprisingly, this theorem yields forward ergodic theorems for countable groups, in particular, one for pmp actions of free groups of finite rank, and can be extended to yield ergodic theorems for pmp actions of free semigroups as well. In each case, the averages are taken along subtrees of the standard Cayley graph rooted at the identity. This is joint work with Anush Tserunyan.

Please find the webpage containing all relevant information below. Registration is optional but strongly encouraged for planning purpose.

https://sites.math.rutgers.edu/~fc327/GLaDF2023/index.html

- - - - Web Site - - - -

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

(site designed, built & maintained by Victoria Gitman)

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

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

## This Week in Logic at CUNY

- - - - Monday, Sep 18, 2023 - - - -

Rutgers Logic Seminar

Monday, Sept 18th, 3:30pm, Rutgers University, Hill 705

Alex Kruckman (Wesleyan)

The complexity of ages admitting a universal limit structure.

Abstract: An age is a hereditary class of finitely generated structures with the joint embedding property which is countable up to isomorphism. If K is an age, a K-limit is a countable structure M such that every finitely generated substructure of M is in K. A K-limit U is universal if every K-limit embeds in U. It is well-known that K has the amalgamation property (AP) if and only if K admits a homogeneous limit (the Fraïssé limit), which is universal. But not every age with a universal limit has AP. We show that, while the existence of a universal limit can be characterized by the well-definedness of a certain ordinal-valued rank on structures in K, it is not equivalent to any finitary diagrammatic property like AP. More precisely, we show that for ages in a fixed sufficiently rich language L, the property of admitting a universal limit is complete coanalytic. This is joint work with Aristotelis Panagiotopoulos.

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

Title: Non-classicality all the way up

Abstract: Nearly all non-classical logics that have been studied admit of classical reasoning about them. For example, in the logic K3, A or not-A is not a valid schema. However, ‘A or not-A’ is K3-valid or not K3-valid—this is, in some sense, a valid claim. In this talk, I introduce a simple framework for thinking about the logic of a given logic. This allows for a measure of the non-classicality of a logic—one on which almost all familiar non-classical logics are of the lowest grade of non-classicality. I’ll then discuss some strategies for generating and theorizing logics of higher grades of non-classicality, as well as some motivation for taking these logics seriously.

- - - - Tuesday, Sep 19, 2023 - - - -

- - - - Wednesday, Sep 20, 2023 - - - -

- - - - Thursday, Sep 21, 2023 - - - -

Infinite Games Workshop

Zoom Talk, details at https://jdh.hamkins.org/infinite-games-workshop/

Thursday 21 September, 11 am

Speaker: Davide Leonessi, The Graduate Center of the City University of New York

Title: Infinite draughts: a solved open game

- - - - Friday, Sep 22, 2023 - - - -