# Set Theory Talks

Global set theory seminar and conference announcements

## Logic Seminar 1 Feb 2023 17:00 hrs at NUS by Yu Liang, Nanjing University

NUS Logic Seminar
Invitation to the Logic Seminar at the National University of Singapore Date: Wednesday, 1 February 2023, 17:00 hrs Place: NUS, Department of Mathematics, S17#05-11 Speaker: Yu Liang Title: Some applications of recursion theory to set theory Abstract: I shall present some recent results in set theory which are based on proof methods and results from recursion theory. URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html

## Reminder for today's Talk

NUS Logic Seminar
The following logic semianr talk is today (now) at 17:00 hrs Singapore time; the talk is only by Zoom. The Zoom Login is this: https://nus-sg.zoom.us/j/83049258042?pwd=UWViaWNvTFUrdFdhOHJCdEVydnVkdz09 Meeting ID: 830 4925 8042 Passcode: 1729=x3+y3 Title and Abstract of today's talk can be found on the following webpage of the logic seminar: https://www.comp.nus.edu.sg/~fstephan/logicseminar.html The title is: Regressive versions of Hindman's Theorem. The speaker is: Leonardo Mainardi. You find on this link also the still free time-slots; if any of you wants to give a talk from overseas, we will make it on Zoom as well; local speakers can also give a physical talk in the meeting. Best regards, Frank

## Cross-Alps Logic Seminar (speaker: Katarzyna Kowalik)

Cross-Alps Logic Seminar
On Friday 27.01.2023 at 16:00
Katarzyna Kowalik (University of Warsaw)
will give a talk on
Reverse mathematics of some Ramsey-theoretic principles over a weak base theory

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 2017 'Mathematical logic: models, sets, computability'.

## This Week in Logic at CUNY

This Week in Logic at CUNY
The CUNY semester starts this week - welcome back, everyone!  I want to draw particular attention to the Fitting at 80 Conference taking place this Saturday, January 28th (see below for details).

Best,
Jonas Reitz

This Week in Logic at CUNY:

- - - - Monday, Jan 23, 2023 - - - -

Rutgers Logic Seminar
Monday, January 23, 2pm, Rutgers University, Hill 005
The Borel complexity of modules

- - - - Tuesday, Jan 24, 2023 - - - -

Models of Peano Arithmetic (MOPA)
Tuesday, January 24, 1:00pm
Virtual (email Victoria Gitman vgitman@nylogic.org for meeting id)

Karel Hrbacek, CUNY
Representation of unlimited integers

Nonstandard methods have been successfully applied to standard problems in number theory by R. Jin, T. Tao and others. A. Boudaoud and D. Bellaouar are pursuing the opposite direction: they are formulating number-theoretic problems in the language of nonstandard analysis and solving them by standard methods. Two examples of the kind of questions they consider are:
(1) Can every unlimited natural number n be represented in the form n = s + w_1w_2 where s is a limited integer and w_1, w_2 are unlimited?
(2) Can every unlimited natural number n be represented in the form n = w_1w_2 + w_3w_4 so that each ratio w_i / w_j is appreciable (ie, neither infinitesimal nor unlimited)?
I give a negative answer to question (1) (assuming Dickson’s Conjecture) and a positive answer to question (2).
A. Boudaoud, D. Bellaouar, Representation of integers: A nonclassical point of view, Journal of Logic & Analysis. 12:4 (2020) 1{31; K. Hrbacek, Journal of Logic & Analysis 12:5 (2020) 1–6.

- - - - Wednesday, Jan 25, 2023 - - - -

- - - - Thursday, Jan 26, 2023 - - - -

- - - - Friday, Jan 27, 2023 - - - -

- - - - Saturday, Jan 28, 2023 - - - -

Fitting at 80
Saturday, January 28

A prominent logician Melvin Fitting has turned 80. This online conference is a special event in his honor. Melvin Fitting was in the departments of Computer Science, Philosophy, and Mathematics at the CUNY Graduate Center and in the department of Mathematics and Computer Science at Lehman College. He is now Professor Emeritus. He has authored 11 books and over a hundred research papers with staggering citation figures. In 2012 Melvin Fitting was given the Herbrand Award by the Conference on Automated Deduction (CADE) for distinguished contributions to the field.

Greetings, congratulations, photos for posting, and ZOOM link requests could be sent to Sergei Artemov by sartemov@gmail.com or sartemov@gc.cuny.edu.

Conference website https://sartemov.ws.gc.cuny.edu/fitting-at-80/

Program (the times are given in the Eastern Day Time zone EST).
January 28, Saturday
8:00-8:45 am Arnon Avron (Tel Aviv), “Breaking the Tie: Benacerraf’s Identification Argument Revisited”
8:45-9:30 am Junhua Yu (Beijing), "Exploring Operators on Neighborhood Models"
9:45-10:30 am Sara Negri (Genoa), "Faithful Modal Embedding: From Gödel to Labelled Calculi"
10:30-11:15 am Heinrich Wansing (Bochum), “Remarks on Semantic Information and Logic. From Semantic Tetralateralism to the Pentalattice 65536_5”
11:30 am -12:15 pm Roman Kuznets (Vienna), "On Interpolation"
12:15-1:00 pm Walter Carnielli (Campinas), “Combining KX4 and S4: A Logic That Encompasses Factive and Non-factive Evidence”
1:15-2:00 pm Eduardo Barrio and Federico Pailos (Buenos Aires), “Meta-classical Non-classical Logics”
2:00-2:45 pm Graham Priest (New York), "Jaśkowski and the Jains: a Fitting Tribute"
2:45-4:00 pm Session of memories and congratulations featuring Sergei Artemov, Hiroakira Ono, Anil Nerode, Melvin Fitting, and others.

Next Week in Logic at CUNY:

- - - - Monday, Jan 30, 2023 - - - -

- - - - Tuesday, Jan 31, 2023 - - - -

Models of Peano Arithmetic (MOPA)
Tuesday, January 31, 1:00pm
Virtual (email Victoria Gitman vgitman@nylogic.org for meeting id)

Lorenzo Galeotti, Amsterdam University College
Order types of models of arithmetic without induction

It is a well-known fact that non-standard models of Peano Arithmetic (PA) have order type N + Z · D, where D is a dense linear order. The question of which dense linear orders D can occur in such order types is non-trivial and widely studied. In this context Friedman asked the following question:

Are there consistent extensions of Peano Arithmetic T and T′ such that the class of order types of models of T and the class of order types of models of T′ differ?

Friedman’s question is very complex and still wide open. In this talk we will go in the opposite direction and consider a version of Friedman’s question for syntactic fragments of PA. We will present results from a joint work with Benedikt Löwe on order types of non-standard models of syntactic subsystems of arithmetic obtained by restricting the language to subsets of the operations. We will put particular emphasis on models of syntactic subsystems of Peano Arithmetic obtained by dropping the schema of induction.

- - - - Wednesday, Feb 1, 2023 - - - -

- - - - Thursday, Feb 2, 2023 - - - -

- - - - Friday, Feb 3, 2023 - - - -

Set Theory Seminar
CUNY Graduate Center, Friday, February 3, 12:30pm NY time
Virtual: Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Jing Zhang, University of Toronto

- - - - Other Logic News - - - -

- - - - Web Site - - - -

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

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

## Wednesday seminar

Prague Set Theory Seminar
Dear all, The seminar meets on Wednesday January 25th at 11:00 in the Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building. Program: David Bradley-Williams -- Limits of betweenness relations and their automorphism groups Some permutation groups are best represented/constructed as kinds-of-products of or limits of simpler permutation groups. We discuss joint work with John Truss (Leeds) in which we construct a family of structures called "limits of betweenness relations" as a kind of tree-limit of trees (for appropriate combinatorial meanings of the word "tree"). A crucial part of the construction is an particular instance of categorical Fraissé Theory. Further we plan to say how their automorphism groups fit into the landscape of infinite primitive Jordan permutation groups and the structure theory of Jordan groups established by S. Adeleke, D. Macpherson, and P. M. Neumann. Best, David PS: Let me also remind you the joint Logic Seminar/Colloquium of the MLTCS department on Monday January 23rd, 16:00, Institute of Mathematics CAS, blue lecture room on the ground floor of the rear building. After the lecture we will go to a pub. Niel Thapen -- Bounded arithmetic and witnessing A witnessing theorem lets you recover, from a proof that an object exists, an algorithm to construct such an object. I will introduce the weak arithmetic theory S^1_2 and describe a simple model-theoretic proof of Buss's witnessing theorem, connecting this theory with polynomial time computations, with some unprovability results that follow from this. I will discuss some open problems about witnessing for stronger bounded theories.

## (KGRC) guests, video, and a talk on Thursday, January 26

Kurt Godel Research Center
The KGRC welcomes as guests: Martin Hils (host: Matthias Aschenbrenner) visits the KGRC until March 31 and gives a talk on January 26, see below. Franz-Viktor Kuhlmann (host: Matthias Aschenbrenner) visits the KGRC until January 31. Jonathan Schilhan (host: Thilo Weinert) visits the KGRC until January 31. Clifton Ealy (host: Matthias Aschenbrenner) visits the KGRC until August 15. Jerzy Kąkol (host: Damian Sobota) visits the KGRC from February 27 to March 3. Manuel López Pellicer (host: Damian Sobota) visits the KGRC from February 27 to March 3. Juris Steprāns (host: Vera Fischer) visits the KGRC from March 6 to March 10 and gives a two-part talk, details to be announced at a later time. * * * For some seminar talks, video recordings are available: "Introduction to big Ramsey degrees" by David Chodounský: https://univienna.zoom.us/rec/share/he-aDDiZDHZJ8Y4Zn_FjiIwdbOf0VN6UKJrxWC7xXAEf6CG_k6Cu_QfM3gQGzwsd.wYq8tUjxaZFywaFK Pass code: @&61nNnR "The weak Ramsey property" by Wiesław Kubiś: https://univienna.zoom.us/rec/share/VeLRgmK7tBdTUOLxgzKjPhh20ErRsjUWp7v6hkNpZtM9Gxe3Xu73_Cc_iTF_AYpL.zDpkipMb7P_vKHwO Pass code: +MkI4HUc "A weak form of Global Choice under the GCH, part II" by Peter Holy: https://univienna.zoom.us/rec/share/xVaRaaDknVfPsyI6D_XZtFsxMjHr8bYSXbup0r6knM3oojoSAFdjipHgPOzN5jVw.8N-UyUkiL2g_6IJj Pass code: gS3%+Hy2 * * * Logic Colloquium Kurt Gödel Research Center Thursday, January 26 "Lang-Weil type bounds in finite difference fields" Martin Hils (Universität Münster, DE) We establish Lang-Weil type bounds for the number of rational points of difference varieties over finite difference fields, in terms of the transformal dimension of the variety and assuming the existence of a smooth rational point. It follows that, working in any non-principle ultraproduct $K$ of finite difference fields, the normalized pseudofinite dimension of a quantifier free partial type $p$ is equal to the transformal dimension of $p$, i.e., to the maximal transformal transcendence degree over $K$ of a realization of $p$. This is joint work with Ehud Hrushovski, Jinhe Ye and Tingxiang Zou. Time and Place Talk at 3:00pm in hybrid mode, in person as well as via Zoom. (Students at Uni Wien are required to attend in person.) Universität Wien Institut für Mathematik Kolingasse 14-16 1090 Wien 1st floor Seminar room 10 Zoom: If you need the Zoom data and have not received the meeting link by the day before the talk, please contact richard.springer@univie.ac.at! (Please direct any other requests about the Zoom session to vera.fischer@univie.ac.at.)

## Logic Seminar Wed 18 Jan 2023 17:00 hrs at NUS by Bakhadyr Khoussainov

NUS Logic Seminar
Hello, there was a mistake, the talk is only in Zoom. Please use this login (also below): > > Link to join the Zoom Meeting > > https://nus-sg.zoom.us/j/83049258042?pwd=UWViaWNvTFUrdFdhOHJCdEVydnVkdz09 > > > > Meeting ID: 830 4925 8042 > > Passcode: 1729=x3+y3 Sorry for the confusion caused. Regards, Frank Stephan On Thu, Jan 12, 2023 at 03:01:35PM +0800, Frank STEPHAN wrote: > Invitation to the Logic Seminar at the National University of Singapore > > Date: Wednesday, 18 January 2022, 17:00 hrs > > Place: NUS, Department of Mathematics, S17#04-05 > Talk via Zoom: > https://nus-sg.zoom.us/j/83049258042?pwd=UWViaWNvTFUrdFdhOHJCdEVydnVkdz09 > Meeting ID: 830 4925 8042 > Passcode: 1729=x3+y3 > > Speaker: Bakhadyr Khoussainov > > Title: Definability of algorithmically presented structures. > > URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html > > We aim to describe the isomorphism types of algorithmically > presented structures in the language of the first order logic. > This is one of the key research topics related to the expressive > power of the first order logic. The focus is on two classes > of structures. The first class is the class of structures for > which the positive atomic diagrams are computably enumerable. > We call these structures positive structures. The second class > is the class of structures for which the negative atomic diagrams > are computably enumerable. We call these structures negative > structures. We investigate definability of positive and negative > structures by sets of sentences quantified with Existential, > Universal, Existential-Universal and Universal-Existential > quantifiers using expansions of languages. >

## Descriptive Set Theory and Dynamics: August 14-25, 2023

Conference
In August 2023 a workshop and a conference on descriptive set theory and dynamics will take place in Warsaw: Workshop (14-18.08.2023, Warsaw) Conference (21-25.08.2023, Warsaw) Both are organized within the thematic semester STRUCTURES devoted to various areas of foundations of mathematics and computer science https://www.impan.pl/en/activities/banach-center/conferences/23-simons-08

## CMU Math Logic Seminar next Tuesday

Carnegie Mellon Logic Seminar
TUESDAY, January 24, 2023 Mathematical Logic Seminar: 3:30-4:30 PM Eastern, Online, Paolo Marimon, Imperial College London Join Zoom Meeting: https://cmu.zoom.us/j/92655324096?pwd=VUhSSlkrdHMxbTlSYUMxYzFXM01kdz09 Meeting ID: 926 5532 4096 Passcode: 555455 TITLE: Invariant Keisler measures in simple omega-categorical structures ABSTRACT: We study invariant Keisler measures in the context of omega-categorical structures. For a first-order structure M, these are finitely additive probability measures on the Boolean algebra of definable subsets Def_x(M) which are invariant under the action of the automorphism group Aut(M). A natural notion of smallness for a definable subset of M is that it is assigned measure 0 by any invariant Keisler measure. Another natural model-theoretic notion of smallness is forking over the empty set. These two notions coincide in various classes of structures, including stable and NIP omega-categorical ones. In a recent article, Chernikov, Hrushovski, Kruckman, Krupinski, Moconja, Pillay and Ramsey find the first examples of simple structures with formulas which do not fork over the empty set but are universally measure zero. I give the first known simple omega-categorical examples exhibiting this property. These are various omega-categorical Hrushovski constructions. In order to prove this, I use a probabilistic independence result by Jahel and Tsankov to show that a stronger version of the independence theorem holds for simple omega-categorical structures where a formula forks over the empty set if and only if it is universally measure zero.

## Wednesday seminar

Prague Set Theory Seminar
Dear all, The seminar meets on Wednesday January 18th at 11:00 in the Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building. There will be a joint Logic Seminar/Colloquium of the MLTCS department on Monday January 23rd, 16:00, Institute of Mathematics CAS, blue lecture room on the ground floor of the rear building. After the lecture we will go to a pub. Everybody will be welcome! Wednesday program: Adam Bartoš -- Isosceles-free homogeneous metric spaces While studying metric spaces in the context of Fraïssé theory we have considered the class of isosceles-free metric spaces: the spaces containing no nondegenerate isosceles triangles. All finite isoceles-free spaces form a hereditary class without weak amalgamation property. Every 1-homogeneous isosceles-free space is already ultrahomogeneous, and we can characterize all such spaces. There are also related decompositions of metric spaces giving bounds on the maximal number of distinct distances in a finite ultrahomogeneous metric space. This is joint work with Christian Bargetz, Wiesław Kubiś, and Franz Luggin. MLTCS seminar: Niel Thapen -- Bounded arithmetic and witnessing A witnessing theorem lets you recover, from a proof that an object exists, an algorithm to construct such an object. I will introduce the weak arithmetic theory S^1_2 and describe a simple model-theoretic proof of Buss's witnessing theorem, connecting this theory with polynomial time computations, with some unprovability results that follow from this. I will discuss some open problems about witnessing for stronger bounded theories. Best, David

## (KGRC) Set Theory Seminar talk on Tuesday, January 17

Kurt Godel Research Center
The KGRC welcomes as guests: Martin Hils (host: Matthias Aschenbrenner) visits the KGRC until March 31, 2023 and gives a talk on January 26, 2023 (details to be announced at a later time). Franz-Viktor Kuhlmann (host: Matthias Aschenbrenner) visits the KGRC until January 31, 2023. Clifton Ealy (host: Matthias Aschenbrenner) visits the KGRC until August 15. Tomasz Żuchowski (host: Damian Sobota) visits the KGRC until January 17. Jerzy Kąkol (host: Damian Sobota) visits the KGRC from February 27 to March 3. Manuel López Pellicer (host: Damian Sobota) visits the KGRC from February 27 to March 3. Juris Steprāns (host: Vera Fischer) visits the KGRC from March 6 to March 10 and gives a two-part talk (details to be announced at a later time). * * * Set Theory Research Seminar Kurt Gödel Research Center Tuesday, January 17 "A weak form of Global Choice under the GCH, part 2" Peter Holy (TU Wien) In 2012, Joel Hamkins asked (on MathOverflow) whether it is possible for the universe of sets to have a linear ordering, but no wellordering (that is, global choice fails). This question, which I consider very interesting, appears to still be open. In my talk, I want to present a somewhat related result. After providing a gentle introduction to second order set theory and the principle of global choice (no knowledge on these matters is assumed), we consider a different weakening of global choice under the GCH: The minimal ordinal-connection axiom MOC due to Rodrigo Freire. It is equivalent to the statement that the universe of sets can be stratified by a subset-increasing hierarchy with each K_alpha of the same size as alpha, and such that K_kappa=H(kappa), the collection of sets of hereditary size less than kappa, for every regular infinite cardinal kappa. In this form, it clearly implies the GCH, and is easily seen to be a weak form of global choice under the GCH. We will show, using class forcing products of adding Cohen subsets of regular cardinals (without assuming any particular knowledge regarding the technique of class forcing), that MOC can consistently fail in models of the GCH, and that MOC can consistently hold while global choice fails. This is joint work with Rodrigo Freire (University of Brasilia). Time and Place Talk at 3:00pm in hybrid mode, in person as well as via Zoom. (Students at Uni Wien are required to attend in person.) Universität Wien Institut für Mathematik Kolingasse 14-16 1090 Wien 1st floor Seminar room 10 Zoom: If you need the Zoom data and have not received the meeting link by the day before the talk, please contact richard.springer@univie.ac.at! (Please direct any other requests about the Set Theory Seminar to vera.fischer@univie.ac.at.)

## Logic Seminar Wed 18 Jan 2023 17:00 hrs at NUS by Bakhadyr Khoussainov

NUS Logic Seminar
Invitation to the Logic Seminar at the National University of Singapore Date: Wednesday, 18 January 2022, 17:00 hrs Place: NUS, Department of Mathematics, S17#04-05 Talk via Zoom: https://nus-sg.zoom.us/j/83049258042?pwd=UWViaWNvTFUrdFdhOHJCdEVydnVkdz09 Meeting ID: 830 4925 8042 Passcode: 1729=x3+y3 Speaker: Bakhadyr Khoussainov Title: Definability of algorithmically presented structures. URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html We aim to describe the isomorphism types of algorithmically presented structures in the language of the first order logic. This is one of the key research topics related to the expressive power of the first order logic. The focus is on two classes of structures. The first class is the class of structures for which the positive atomic diagrams are computably enumerable. We call these structures positive structures. The second class is the class of structures for which the negative atomic diagrams are computably enumerable. We call these structures negative structures. We investigate definability of positive and negative structures by sets of sentences quantified with Existential, Universal, Existential-Universal and Universal-Existential quantifiers using expansions of languages.

## Core Model Seminar starting again in two weeks

Carnegie Mellon Logic Seminar
TUESDAY, January 24, 2023 Core Model Seminar: 1:30-3 PM Eastern, Online, Takehiko Gappo, TU Wien Join Zoom Meeting: https://cmu.zoom.us/j/97749733438?pwd=Yk5PcSsvekptWWxMNUhCU2pFbzA0Zz09 Meeting ID: 977 4973 3438 Passcode: 457791 TITLE: Chang models over derived models ABSTRACT: We will give a proof outline of the main theorem in Sargsyan's paper, "Covering with Chang models over derived models." In this paper, he constructed a new model of determinacy extending the derived model, called the Chang model over the derived model, inside of a symmetric extension of a least branch hod mouse with Woodin cardinals. This result will be used in the next talk. TUESDAY, January 31, 2023 Core Model Seminar: 1:30-3 PM Eastern, Online, Takehiko Gappo, TU Wien Join Zoom Meeting: https://cmu.zoom.us/j/97749733438?pwd=Yk5PcSsvekptWWxMNUhCU2pFbzA0Zz09 Meeting ID: 977 4973 3438 Passcode: 457791 TITLE: Determinacy in the Chang model from a hod pair ABSTRACT: We will show that the Chang model satisfies determinacy from the existence of an excellent least branch hod pair with a Woodin limit of Woodin cardinals. The proof is based on Sargsyan's result on Chang models over derived models. This is joint work with Sargsyan. TUESDAY, February 7, 2023 Core Model Seminar: 1:30-3 PM Eastern, Online, Gabriel Goldberg, University of California, Berkeley Join Zoom Meeting: https://cmu.zoom.us/j/97749733438?pwd=Yk5PcSsvekptWWxMNUhCU2pFbzA0Zz09 Meeting ID: 977 4973 3438 Passcode: 457791 TITLE: TBA; ABSTRACT: TBA TUESDAY, February 14, 2023 Core Model Seminar: 1:30-3 PM Eastern, Online, Gabriel Goldberg, University of California, Berkeley Join Zoom Meeting: https://cmu.zoom.us/j/97749733438?pwd=Yk5PcSsvekptWWxMNUhCU2pFbzA0Zz09 Meeting ID: 977 4973 3438 Passcode: 457791 TITLE: TBA; ABSTRACT: TBA

## Cross-Alps Logic Seminar for World Logic Day (speaker: Vasco Brattka)

Cross-Alps Logic Seminar

On Friday 13.01.2023 at 16:00

on the occasion of World Logic Day 2023, a special session of the Cross-Alps Logic Seminars will take place, with special guest
Vasco Brattka (Universität der Bundeswehr München)
who will give a talk on
Some fascinating topics in logic around reducibilities

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 2017 'Mathematical logic: models, sets, computability'.

## Wednesday seminar

Prague Set Theory Seminar
Dear all, The seminar meets on Wednesday January 11th at 11:00 in the Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building. Program: Jaroslav Supina -- Katětov order on ideals and the Fréchet-Urysohn property We show that the Katětov order on ideals on natural numbers is a useful tool in answering a question posed by J. Gerlits and Zs. Nagy and two questions by M. Sakai. The questions are related to local topological properties of a space of all continuous functions on an underlying topological space, the most known among them being the Fréchet-Urysohn property. This is a joint work with S. Bardyla and L. Zdomskyy. Best, David

## (KGRC) seminar talks Tuesday, January 10 and Thursday, January 12

Kurt Godel Research Center

## Wednesday seminar

Prague Set Theory Seminar
Dear all, The seminar meets on Wednesday January 4th at 11:00 in the Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building. Program: Jonathan Cancino Manriquez -- Ideal independent families and ultrafilters A family X of infinite subsets of natural numbers is an ideal independent family if no element of X is almost contained in the union of finitely many other sets in the family X. The ideal independence number, s_mm, is defined as the minimal cardinality of an ideal independent family. These notions were introduced by D. Monk several years ago, and in joint work with O. Guzmán and A. Miller it was proved that the dominating number is a lower bound for s_mm, among other things. In recent work with V. Fischer and C. B. Switzer it was proved that the ultrafilter number is a lower bound for s_mm, that the spectrum of ideal independent families can be quite wide and also a preservation theorem for ideal independent families along countable support iterations. In this talk we will review some of these results. Best, David

## Nankai Logic Colloquium

Nankai Logic Colloquium

Hello everyone,

Happy Holiday! This is going to be the last event this semester. Our Nankai Logic Colloquium is going to be resumed on Feb.10, 2023.

This week our weekly Nankai Logic Colloquium is going to be in the morning but at a different time.

Our speaker this week will be Liang Yu from Nanjing University. This talk is going to take place this Friday,  Dec 30, 2022,  from 10 am to 11 am(UTC+8, Beijing time)

Title: Some applications of recursion theory to descriptive set theory.

Abstract: We present some applications of recursion theory to descriptive set theory.

___________________________________________________________________________________________________________________________________________________

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

Title：                 The 14th Nankai Logic Colloquium --Liang Yu

Time：                10:00am, Dec. 30, 2022 (Beijing Time)

Zoom Number： 853 2314 4903

Passcode：         153780

_____________________________________________________________________

Best wishes,

Ming Xiao

## Wednesday seminar

Prague Set Theory Seminar
Dear all, The seminar meets on Wednesday December 21st at 11:00 in the Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building. After the seminar the Christmas meeting of employees and friends of the Institute starts at 16:00 in the blue lecture hall. Program: David Chodounsky -- Big Ramsey degrees of metric spaces Hubicka developed a new method for proving finiteness of Big Ramsey degrees of universal structures via the Carlson–Simpson theorem. Using this method we derive a new condition for structures in binary languages which implies finite big Ramsey degrees. In particular, for a given finite set of distances the countable universal metric space with only these distances satisfies the condition. Joint work with Martin Balko, Jan Hubicka, Matej Konecny, Jaroslav Nesetril, and Lluis Vena https://arxiv.org/abs/2105.12184 Best, David

## Nankai Logic Colloquium

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 Selivanov from the A.P. Ershov Institute of Informatic Systems. This talk is going to take place this Friday, Dec 23, 2022,  from 16:00 to 17:00 (UTC+8, Beijing time).

Title: Effective descriptive theory of quasi-Polish spaces

Abstract: Quasi-Polish spaces appeared about ten years ago as a natural extension of Polish spaces which includes many non-Hausdorff spaces of interest to mathematics and computer science (like omega-continuous domains and countably based spectral spaces). In this talk we give a partial survey of results in descriptive set theory of quasi-Polish spaces, including some recent results on effective descriptive set theory and Wadge hierarchy. We will also mention possible new research directions and open questions.

___________________________________________________________________________________________________________________________________________________

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

Title：                 The 13th Nankai Logic Colloquium --Victor Selivanov
Time：                16:00pm, Dec. 23, 2022 (Beijing Time)
Zoom Number：843 9471 9093
Passcode：         481891

_____________________________________________________________________

Best wishes,

Ming Xiao

## This Week in Logic at CUNY - Special announcement: Logic at JMM

This Week in Logic at CUNY
Hi everyone,

I wanted to pass along the following information on logic events at the Joint Mathematics Meetings in early January.

Best,
Jonas

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

The Joint Mathematics Meetings will be held in Boston next month (January 4-7, 2023). We’re very pleased that there will be a full slate of logic events, and we thought you might like to see the list.

1. Definability, Computability, and Model Theory: A Special Session dedicated to Gerald E. Sacks
https://www.jointmathematicsmeetings.org/meetings/national/jmm2023/2270_program_ss51.html

This special session is dedicated both to Prof. Sacks' memory and to his wide mathematical influence. It will include talks in a range of mathematical areas, including computability theory, model theory, and set theory.

Session I: Wednesday January 4, 2023, 8:00 a.m.-12:00 p.m.
Session II: Wednesday January 4, 2023, 1:00 p.m.-6:00 p.m.
Session III: Thursday January 5, 2023, 8:00 a.m.-12:00 p.m.

Independence East, Sheraton Boston Hotel

Organizers: Nathanael L. Ackerman, Cameron E. Freer, Theodore A. Slaman

Speakers: John T. Baldwin, Lenore Blum, Johanna N. Y. Franklin, Marcia Groszek, Valentina Harizanov, Steve Homer, A. Kanamori, Manuel Lerman, Montgomery Link, Robert S. Lubarsky, Maryanthe Malliaris, Rahim Nazim Moosa, Anil Nerode, Richard A. Shore, Stephen G. Simpson, Carol Saunders Wood

----

2. ASL Special Session on Model-theoretic and "Higher Infinite" Methods in Descriptive Set Theory and Related Areas
https://www.jointmathematicsmeetings.org/meetings/national/jmm2023/2270_program_aslss1.html

Thursday January 5, 2023, 1:00 p.m.-5:00 p.m.
306, Hynes Convention Center

Organizers: Rehana Patel, Alexander Kechris, Alejandro Poveda, Assaf Shani

Speakers: Dana Bartosova, Tom Benhamou, Filippo Calderoni, Michael Chris Laskowski, Aristotelis Panagiotopoulos, Forte Shinko, Dima Svetosla Sinapova, Jenna Zomback

----

3. ASL Special Session on Tame Geometry and Applications to Analysis
https://www.jointmathematicsmeetings.org/meetings/national/jmm2023/2270_program_aslss2.html#title

Thursday January 5, 2023, 8:00 a.m.-12:00 p.m.
306, Hynes Convention Center

Organizers: Alexi Block Gorman, Elliot Kaplan, Daniel Miller

Speakers: Chris Miller, Adele Padgett, Nigel Pynn-Coates, Ary Shaviv, Margaret E. M. Thomas, Siegfried Van Hille

----

4. ASL Tutorial: Hilbert's Tenth Problem: Between logic and number theory
https://meetings.ams.org/math/jmm2023/meetingapp.cgi/Program/1081

Session I: Wednesday January 4, 2023, 9:00 a.m.-10:00 a.m.
Session II: Wednesday January 4, 2023, 1:00 p.m.-2:00 p.m.
306, Hynes Convention Center

Speaker: Sylvy Anscombe

----

5. ASL Invited Talks

Friday January 6 and Saturday January 7, 2023
306, Hynes Convention Center

Program Committee: Dana Bartošová, Kirsten Eisenträger, James Freitag (chair) and Philipp Hieronymi

Speakers: Jeremy David Avigad, Peter Cholak, Franziska Jahnke, Sandra Müller, Lynn Scow, Assaf Shani, Erik Donal Walsberg

----

6. ASL Contributed Paper Session
https://www.jointmathematicsmeetings.org/meetings/national/jmm2023/2270_program_friday.html#2270:ASLCP1A

Friday January 6, 2023, 3:00 p.m.-6:00 p.m.
306, Hynes Convention Center

Organizer: David Reed Solomon

Speakers: Athar Abdul-Quader, Jananan Arulseelan, Katalin Bimbo, Daniel Mourad, Carl Mummert, Dan Turetsky

## Wednesday seminar

Prague Set Theory Seminar
Dear all, The seminar meets on Wednesday December 14th at 11:00 in the Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building. There is no fixed program yet. Walk-in speakers will be welcomed. Best, David

## Nankai Logic Colloquium

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 Luca Motto Ros from the University of Turin. This talk is going to take place this Friday, Dec.16.2022,  from 16:00 to 17:00 (UTC+8, Beijing time).

Title

Universality properties of graph homomorphism: one construction to prove them all

Abstract

We show that the natural operation of connected sum for graphs can be used to prove at once most of the universality results from the literature concerning graph homomorphism. In doing so, we significantly improve many existing theorems and we also solve some natural open problems. Despite its simplicity, our technique unexpectedly leads to applications in quite diverse areas of mathematics, such as category theory, combinatorics, classical descriptive set theory, generalized descriptive set theory, model theory, and theoretical computer science.

___________________________________________________________________________________________________________________________________________________

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

Title：                 The 12th Nankai Logic Colloquium -- Luca Motto Ros

Time：                16:00pm, Dec. 16, 2022 (Beijing Time)

Zoom Number：880 9576 5955

Passcode：         289312

_____________________________________________________________________

Best wishes,

Ming Xiao

## This Week in Logic at CUNY

This Week in Logic at CUNY
Hi everyone,

This Wednesday's talk in the The New York City Category Theory Seminar has been postponed until Spring.  As final exams begin this week at CUNY, I believe there are no further talks scheduled until after the New Year.  This Week in Logic will resume regular mailings at the end of January 2023.

Happy Holidays to all!
Jonas

This Week in Logic at CUNY:

- - - - Monday, Dec 12, 2022 - - - -

- - - - Tuesday, Dec 13, 2022 - - - -

- - - - Wednesday, Dec 14, 2022 - - - -

- - - - Thursday, Dec 15, 2022 - - - -

- - - - Friday, Dec 16, 2022 - - - -

Next Week in Logic at CUNY:

- - - - Monday, Dec 19, 2022 - - - -

- - - - Tuesday, Dec 20, 2022 - - - -

- - - - Wednesday, Dec 21, 2022 - - - -

- - - - Thursday, Dec 22, 2022 - - - -

- - - - Friday, Dec 23, 2022 - - - -

- - - - Other Logic News - - - -

- - - - Web Site - - - -

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

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

## (KGRC) CORRECTED: seminar talks Tuesday, December 13 and Thursday, December 15

Kurt Godel Research Center

## This Week in Logic at CUNY

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

- - - - Monday, Dec 5, 2022 - - - -

Rutgers Logic Seminar
Monday, December 5, 3:30pm, Rutgers University, Hill 705
Takehiko Gappo, Rutgers
Determinacy in the Chang model from a hod pair

Logic and Metaphysics Workshop
Date: Monday, November 28, 4.15-6.15 (NY time), GC 7314
Martin Pleitz (Muenster)
Title: Reification as identity?

Abstract: Abstract objects like properties and propositions, I believe, are the result of reification, which can intuitively be characterized as the metaphysical counterpart of nominalization (as in the shift, e.g., from ‘is a horse’ to ‘the property of being a horse’; cf. Schiffer, Moltmann), and occurs paradigmatically in the well-known bridge laws for instantiation, truth, etc. (e.g., something instantiates the property of being a horse iff it is a horse). So far, I have been working on an account of reification in terms of the technical notions of encoding & decoding, as some regulars at the L+M workshop may recall. In my upcoming talk, I wish to embed reification more clearly in higher-order metaphysics and explore an alternative idea: Can reification be construed as identification across metaphysical categories? E.g., can the object that is the property of being a horse be identified, in some sense, with Frege’s concept horse, which is a non-objectual item because ‘is a horse’ is not a singular term? In my presentation I will argue for an affirmative answer. For this, I will sketch an ultra-generalized logic of equivalence, which has as its special cases (i) the well-known logics of first-order identity and equivalence, (ii) recent logics of generalized identities (à la Rayo, Linnebo, Dorr, Fine, Correia, Skiles, …) which connect higher-order items of the same type, and (iii) the logic of my proposed cross-level equivalences which connect items of different types. In a second step, I will re-construe reification as the cross-level equivalence that holds between higher-order items and abstract objects of the appropriate sort and argue that this account of reification as identity has certain advantages.

- - - - Tuesday, Dec 6, 2022 - - - -

- - - - Wednesday, Dec 7, 2022 - - - -

The New York City Category Theory Seminar
Department of Computer Science
Department of Mathematics
The Graduate Center of The City University of New York

Speaker:     Robert Pare, Dalhousie University.

Date and Time:     Wednesday December 7, 2022, 7:00 - 8:30 PM.

Title:     The horizontal/vertical synergy of double categories.

Abstract: A double category is a category with two types of arrows, horizontal and vertical, related by double cells. Think of sets with functions and relations as arrows and implications as double cells. The theory is 2-dimensional just like for 2-categories. In fact 2-categories were originally defined as double categories in which all vertical arrows were identities. Most of the theory of 2-categories extends to double categories resulting in a deeper understanding. This is one aspect of double categories: they’re “new and improved” 2-categories.

From a purely formal point of view, a double category is a category object in CAT. Once a familiarity with double categories has developed, it is amusing and instructive to see how the various constructs of formal category theory play out in this setting.

But these two aspects of double categories, fancy 2-categories or internal categories, are only part of the picture. Perhaps the most important thing is the interplay between the horizontal and the vertical.

I will start with some examples of double categories to give a feeling for the objects I will be discussing, and then look at several concepts indicative of the rich interplay between the horizontal and the vertical.

- - - - Thursday, Dec 8, 2022 - - - -

- - - - Friday, Dec 9, 2022 - - - -

Set Theory Seminar
CUNY Graduate Center, Friday, December 9, 12:15pm NY time
Virtual: Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Vladimir Kanovei Institute for Information Transmission Problems

On the significance of parameters in the comprehension and choice schemata in second-order arithmetic

Parameters are free variables in various axiom schemata in PA, ZFC, and other similar theories. Given an axiom schema S, we let S* be the parameter-free sub-schema.

Kreisel (A survey of proof theory, JSL 1968) was one of those who paid attention to the comparison of some schemata in second-order PA and their parameter-free versions. In particular, Kreisel noted that
[...] if one is convinced of the significance of something like a given axiom schema, it is natural to study details, such as the effect of parameters.

This talk is devoted to the effect of parameters in the schemata of Comprehension and Choice in second-order arithmetic.

Logic Workshop
Hybrid: Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Friday December 9, 2:00pm-3:30pm, Room 6417
Daniel Turetsky, Victoria University of Wellington
Wadge degrees, games, and the separation and reduction properties

In this talk, I will give an overview of the picture of the Borel Wadge degrees. Our system of descriptions allows us to describe their Delta-classes, as well as specify which degrees have the separation or reduction properties. Part of our analysis is based on playing games along our descriptions, and so I will explain how these games are played and what they can tell us.

Next Week in Logic at CUNY:

- - - - Monday, Dec 12, 2022 - - - -

- - - - Tuesday, Dec 13, 2022 - - - -

- - - - Wednesday, Dec 14, 2022 - - - -

The New York City Category Theory Seminar
Department of Computer Science
Department of Mathematics
The Graduate Center of The City University of New York
Speaker:     Gemma De las Cuevas, University of Innsbruck.
Date and Time:     Wednesday December 14, 2022, 7:00 - 8:30 PM.
Title:     A framework for universality across disciplines.

Abstract: What is the scope of universality across disciplines? And what is its relation to undecidability? To address these questions, we build a categorical framework for universality. Its instances include Turing machines, spin models, and others. We introduce a hierarchy of universality and argue that it distinguishes universal Turing machines as a non-trivial form of universality. We also outline the relation to undecidability by drawing a connection to Lawvere’s Fixed Point Theorem. Joint work with Sebastian Stengele, Tobias Reinhart and Tomas Gonda.

- - - - Thursday, Dec 15, 2022 - - - -

- - - - Friday, Dec 16, 2022 - - - -

- - - - Other Logic News - - - -

Post doc in logic/metaphysics:
**JOB: 6-Month Visiting Fellowship at the Complutense University of Madrid**

The Project “Unstable Metaphysics” led by Elia Zardini and Sergi Oms at the Department of Logic and Theoretical Philosophy of the Complutense University of Madrid is pleased to offer a Postdoctoral Visiting Fellowship for six months starting in early 2023 (the exact start is somewhat flexible). The fellow will work on applications of nonclassical logics to metaphysics. The exact amount of the net salary will depend on the circumstances of the successful applicant, but can be expected to be around 1,400 EUR per month.

To be considered, applicants should submit their (1) CV, (2) PhD certificate (or declaration concerning submission of PhD thesis) and (3) a short (max 1,000 words) research proposal on the above-mentioned topic to ezardini@ucm.es no later than December 11th 2022 (informal inquiries can be directed to the same email address).

- - - - Web Site - - - -

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

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

## Wednesday seminar

Prague Set Theory Seminar
Dear all, The seminar does not meet next week, Wednesday December 7th. (Some regular seminar participants are away.) The seminar should meet again on Wednesday December 14th. Best, David

## Upcoming core model seminar

Carnegie Mellon Logic Seminar
TUESDAY, December 6, 2022 Core Model Seminar: 1:30 - 3 PM Eastern, Online, Gabriel Goldberg, University of California, Berkeley Join Zoom Meeting: https://cmu.zoom.us/j/97749733438?pwd=Yk5PcSsvekptWWxMNUhCU2pFbzA0Zz09 Meeting ID: 977 4973 3438 Passcode: 457791 TITLE: External ultrapowers of HOD in models of determinacy ABSTRACT: We show that in L(R) under determinacy, the external ultrapower of HOD^L(R) by a countably complete ultrafilter on an ordinal less than theta^L(R) is a normal iterate of HOD^L(R) via its iteration strategy. This is joint work with Grigor Sargsyan. ORGANIZERS' NOTE: This is the final meeting of 2022 after which the seminar will resume on January 24, 2023.

## (KGRC) two talks in the Set Theory Seminar on Tuesday, December 6

Kurt Godel Research Center

## (KGRC) talks Tuesday, November 29 and Wednesday, November 30

Kurt Godel Research Center
The KGRC welcomes as guests: Martin Hils (host: Matthias Aschenbrenner) visits the KGRC until March 31, 2023 and gives a talk on January 19, 2023 (details to be announced at a later time). Franz-Viktor Kuhlmann (host: Matthias Aschenbrenner) visits the KGRC until January 31, 2023. David Chodounsky (host: Vera Fischer) visits the KGRC from December 4 until December 8 and gives a talk on December 6 (details to be announced at a later time). Jan Hubicka (host: Vera Fischer) visits the KGRC from December 5 until December 8 and gives a talk on December 6 (details to be announced at a later time). Stefan Ludwig (hosts: Martin Hils and Matthias Aschenbrenner) visits the KGRC from December 5 to December 14. * * * FG1 Seminar Institute of Discrete Mathematics and Geometry, TU Wien Tuesday, November 29 "Large cardinals and properties of generalized logics" Menachem Magidor (Hebrew University of Jerusalem, IL) This is a joint work with Will Boney, Stamis Dimipoulos and Victoria Gitman. It is well known that many large cardinals properties and schemata can be phrased as regularities properties of generalized logics. (Typical examples are Skolem-Löwenheim and compactness properties.) In this talk we shall present some additional such characterizations. An example is the connection between subtle cardinals and the existence of weak compactness for every abstract logic or the characterization of various virtual cardinals in terms of variations of compactness properties appropriate for the context of virtual large cardinals. Time and Place Talk at 9:00am TU Wien Institut für Diskrete Mathematik und Geometrie Wiedner Hauptstrasse 8-10 Turm A (green) 8th floor Dissertantenraum Please direct any questions about this talk to algebra@dmg.tuwien.ac.at. * * * Set Theory Research Seminar Kurt Gödel Research Center Tuesday, November 29 "Subversion Forcing" Corey Switzer (KGRC) In these two talks we will introduce Jensen's classes of subcomplete and subproper forcing as well as discuss some applications due to the speaker and Fuchs, and the speaker and Sakai. An important feature of proper forcing is the countable covering property: every countable set of ordinals added by a proper forcing notion is contained in a ground model countable set of ordinals. This is important in iteration theorems. Subproper forcing is a weakening of proper forcing that is still iterable while including some well known forcing notions which do add countable sets of ordinals that are not covered by anything in the ground model including Namba forcing (under CH) and Prikry forcing. One can weaken other classes of forcing notions in a similar way and the "sub"version of the countably closed forcing, known as subcomplete forcing, is a particularly interesting subclass of subproper forcing that was used by Jensen in several applications including his solution to the extended Namba problem. In the first of these talks I will introduce the classes subproper and subcomplete forcing as well as discuss simplifications of them due to Fuchs and myself. Time permitting I will discuss new iterations theorems for these classes reminiscent of similar theorems proved for proper forcing in the context of the reals and combinatorics on $\omega_1$ ($\omega^\omega$-bounding, preservation of Souslin trees etc). In the second talk I will discuss the forcing axioms for these classes including their applications and limitations. In particular, time permitting, I will discuss a recent result, joint with Hiroshi Sakai that the forcing axiom for subcomplete forcing is compatible with a $\square_{\omega_1}$-sequence. The take away is a class of strong forcing axioms that are compatible with a wide variety of behaviour on the level of the reals and combinatorics on cardinals below the continuum. Time and Place Talk at 3:00pm in hybrid mode, in person as well as via Zoom. (Students at Uni Wien are required to attend in person.) Universität Wien Institut für Mathematik Kolingasse 14-16 1090 Wien 1st floor Seminar room 10 Zoom: If you need the Zoom data and have not received the meeting link by the day before the talk, please contact richard.springer@univie.ac.at! (Please direct any other requests about this talk to vera.fischer@univie.ac.at.) * * * Mathematisches Kolloquium Faculty of Mathematics Wednesday, November 30 "Regularity properties of subsets of the real line and other polish spaces" Menachem Magidor (Hebrew University of Jerusalem, IL) Using the axiom of choice one can construct set of reals which are pathological in some sense. Similar constructions can produce such "pathological" subsets of any non-trivial Polish space (= a complete separable metric space). Typical examples of "pathology" is the set being non-measurable, lacking the property of Baire (= not equivalent to an open set modulo meager set), being a counter example to generalizations of Ramsey theorem. A subset of the Baire space N^N is "pathological" if in the associated game, no player has a winning strategy. A prevailing paradigm in Descriptive Set Theory is that sets that has a "simple description" should not be pathological. Evidence for this maxim is the fact that Borel sets are not pathological in any of the senses described above. In this talk we shall present a notion of "super regularity" for subsets of a Polish space, the family of universally Baire sets. The universally Baire sets typically do not show the "pathologies" we listed above, especially if one assumes the existence of large cardinals. We shall try to describe the deep impact that the existence of the large cardinals has on the structure of definable sets of reals and universally Baire sets. The talk should be accessible to a wide mathematical audience. Time and Place Coffee at 3:45pm Talk at 4:15pm Faculty of Mathematics Oskar-Morgenstern-Platz 1 1090 Vienna 12th floor Sky Lounge Please direct any questions about this talk to vera.fischer@univie.ac.at.

## Wednesday seminar

Prague Set Theory Seminar
Dear all, The seminar meets on Wednesday November 30th at 11:00 in the Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building. There is no fixed program yet. Walk-in speakers will be welcomed. Best, David

## Cross-Alps Logic Seminar (speaker: Francesco Parente)

Cross-Alps Logic Seminar
On Friday 2.12.2022 at 16:00
Francesco Parente (University of Turin)
will give a talk on
Good ultrafilters and universality properties of forcing

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 2017 'Mathematical logic: models, sets, computability'.

## Nankai Logic Colloquium

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  Todor Tsankov from Université Lyon 1. This talk is going to take place this Friday,  Dec.02.2022,  from 4 pm to 5 pm (UTC+8, Beijing time).

Title: Extremal models in affine logic

Abstract: Affine logic is a fragment of continuous logic, introduced by Bagheri,
where one allows only affine functions R^n -> R as connectives instead
of arbitrary continuous functions. This decreases the expressive power
of the logic and provides additional structure on the type spaces:
namely, the structure of compact, convex sets. An important role in
convex analysis is played by the extreme points of these sets and,
unsurprisingly, extremal models, in which only extreme types are
realized, are crucial for developing affine model theory.

In a joint work with Itaï Ben Yaacov and Tomás Ibarlucía, we develop
the basic theory of extremal models. Some highlights include a general
integral decomposition theorem (generalizing the ergodic decomposition
theorem from ergodic theory) and affine aleph_0-categoricity:
theories admitting a unique separable, extremal model.

In the talk, I will give a gentle introduction to affine logic and will
explain some of our main results.

___________________________________________________________________________________________________________________________________________________

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

Title：                 The 11th Nankai Logic Colloquium -- Todor Tsankov

Time：                16:00pm, Dec. 2, 2022 (Beijing Time)

Zoom Number：817 7281 1616

Passcode：         468722

_____________________________________________________________________

Best wishes,

Ming Xiao

## This Week in Logic at CUNY

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

- - - - Monday, Nov 28, 2022 - - - -

Logic and Metaphysics Workshop
Date: Monday, November 28, 4.15-6.15 (NY time), GC 7314
William McCarthy (Columbia).

Title: Modal pluralism and higher-order logic

Abstract: Modal pluralism is the view that there are a variety of candidate interpretations of the predicate ‘could have been the case that’ which give intuitively different answers to paradigmatic metaphysical questions (‘intuitively’ because the phrase means subtly different things on the different interpretations). It is the modal analog of set-theoretic pluralism, according to which there are a variety of candidate interpretations of ‘is a member of’.  Of course, if there were a broadest kind of counterfactual possibility, then one could define every other kind as a restriction on it, as in the set-theoretic case.  It would then be privileged in the way that a broadest kind of set would be, if there were one.  Recently, several authors have purported to prove from higher-order logical principles that there is a broadest kind of possibility. In this talk we critically assess these arguments.  We argue that they rest on an assumption which any modal pluralist should reject: namely, monism about higher-order logic. The reasons to be a modal pluralist are also reasons to be a pluralist about higher-order quantification. But from the pluralist perspective on higher-order logic, the claim that there is a broadest kind of possibility is like the Continuum Hypothesis, according to the set-theoretic pluralist.  It is true on some interpretations of the relevant terminology, and false on others.  Consequently, the significance of the ‘proof’ that there is a broadest kind of possibility is deflated.  Time permitting, we will conclude with some upshots of higher-order pluralism for the methodology of metaphysics.

Note: This is joint work with Justin Clarke-Doane.

- - - - Tuesday, Nov 29, 2022 - - - -

- - - - Wednesday, Nov 30, 2022 - - - -

- - - - Thursday, Dec 1, 2022 - - - -

- - - - Friday, Dec 2, 2022 - - - -

Set Theory Seminar
CUNY Graduate Center, Friday, December 2, 12:15pm NY time
Virtual: Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Will Boney Texas State University

Logic Workshop
Hybrid: Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Friday December 2, 2:00pm-3:30pm, Room 6417
Michał Tomasz Godziszewski University of Vienna

Next Week in Logic at CUNY:

- - - - Monday, Dec 5, 2022 - - - -

Rutgers Logic Seminar
Monday, December 5, 3:30pm, Rutgers University, Hill 705
Takehiko Gappo, Rutgers
Determinacy in the Chang model from a hod pair

Logic and Metaphysics Workshop
Date: Monday, November 28, 4.15-6.15 (NY time), GC 7314
Martin Pleitz (Muenster)
Title: Reification as identity?

Abstract: Abstract objects like properties and propositions, I believe, are the result of reification, which can intuitively be characterized as the metaphysical counterpart of nominalization (as in the shift, e.g., from ‘is a horse’ to ‘the property of being a horse’; cf. Schiffer, Moltmann), and occurs paradigmatically in the well-known bridge laws for instantiation, truth, etc. (e.g., something instantiates the property of being a horse iff it is a horse). So far, I have been working on an account of reification in terms of the technical notions of encoding & decoding, as some regulars at the L+M workshop may recall. In my upcoming talk, I wish to embed reification more clearly in higher-order metaphysics and explore an alternative idea: Can reification be construed as identification across metaphysical categories? E.g., can the object that is the property of being a horse be identified, in some sense, with Frege’s concept horse, which is a non-objectual item because ‘is a horse’ is not a singular term? In my presentation I will argue for an affirmative answer. For this, I will sketch an ultra-generalized logic of equivalence, which has as its special cases (i) the well-known logics of first-order identity and equivalence, (ii) recent logics of generalized identities (à la Rayo, Linnebo, Dorr, Fine, Correia, Skiles, …) which connect higher-order items of the same type, and (iii) the logic of my proposed cross-level equivalences which connect items of different types. In a second step, I will re-construe reification as the cross-level equivalence that holds between higher-order items and abstract objects of the appropriate sort and argue that this account of reification as identity has certain advantages.

- - - - Tuesday, Dec 6, 2022 - - - -

- - - - Wednesday, Dec 7, 2022 - - - -

The New York City Category Theory Seminar
Department of Computer Science
Department of Mathematics
The Graduate Center of The City University of New York

Speaker:     Robert Pare, Dalhousie University.

Date and Time:     Wednesday December 7, 2022, 7:00 - 8:30 PM.

Title:     The horizontal/vertical synergy of double categories.

Abstract: A double category is a category with two types of arrows, horizontal and vertical, related by double cells. Think of sets with functions and relations as arrows and implications as double cells. The theory is 2-dimensional just like for 2-categories. In fact 2-categories were originally defined as double categories in which all vertical arrows were identities. Most of the theory of 2-categories extends to double categories resulting in a deeper understanding. This is one aspect of double categories: they’re “new and improved” 2-categories.

From a purely formal point of view, a double category is a category object in CAT. Once a familiarity with double categories has developed, it is amusing and instructive to see how the various constructs of formal category theory play out in this setting.

But these two aspects of double categories, fancy 2-categories or internal categories, are only part of the picture. Perhaps the most important thing is the interplay between the horizontal and the vertical.

I will start with some examples of double categories to give a feeling for the objects I will be discussing, and then look at several concepts indicative of the rich interplay between the horizontal and the vertical.

- - - - Thursday, Dec 8, 2022 - - - -

- - - - Friday, Dec 9, 2022 - - - -

Set Theory Seminar
CUNY Graduate Center, Friday, December 9, 12:15pm NY time
Virtual: Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Vladimir Kanovei Institute for Information Transmission Problems

Logic Workshop
Hybrid: Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Friday December 9, 2:00pm-3:30pm, Room 6417
Daniel Turetsky, Victoria University of Wellington
Wadge degrees, games, and the separation and reduction properties

In this talk, I will give an overview of the picture of the Borel Wadge degrees. Our system of descriptions allows us to describe their Delta-classes, as well as specify which degrees have the separation or reduction properties. Part of our analysis is based on playing games along our descriptions, and so I will explain how these games are played and what they can tell us.

- - - - Other Logic News - - - -

- - - - Web Site - - - -

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

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

## Core model seminar on Tuesday

Carnegie Mellon Logic Seminar
TUESDAY, November 29, 2022 Core Model Seminar: 1:30 - 3 PM Eastern, Online, Benjamin Siskind, Carnegie Mellon University Join Zoom Meeting: https://cmu.zoom.us/j/97749733438?pwd=Yk5PcSsvekptWWxMNUhCU2pFbzA0Zz09 Meeting ID: 977 4973 3438 Passcode: 457791 TITLE: Full normalization and HOD^L(R) ABSTRACT: We'll review some aspects of the HOD analysis of L(R) and introduce the full normalization machinery developed by Steel and Schlutzenberg. We'll use this to show that HOD^L(R)|theta is actually a normal iterate of M_omega|delta via M_omega's canonical iteration strategy (and a bit more), a result of Steel and Schlutzenberg. Time permitting, we may discuss other applications of full normalization, due to Steel.

## Nankai Logic Colloquium

Nankai Logic Colloquium
Hello everyone,

There is no NLC this week. Instead...the Chinese Annual Conference on Mathematical Logic (CACML 2022) will be held from Nov. 25 to Nov. 27 (UTC+5, Beijing Time)!

This conference is hosted by the Mathematical Logic Professional Committee of the Chinese Mathematical Society and organized by the Anhui Polytechnic University. The purpose of the conference is to provide a platform for scholars of mathematical logic and its applications to report the latest achievements, and carry out extensive academic exchanges and cooperation, so as to promote the development of mathematical logic in China.

This conference plans to set up (but not limited to)  the following topics: (1) set theory, (2) recursion theory, (3) model theory, (4) philosophy of mathematics. The conference will invite domestic and foreign experts in the field of mathematical logic to make thematic reports on the above topics.

Best wishes,
Ming Xiao

## This Week in Logic at CUNY

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

- - - - Monday, Nov 21, 2022 - - - -

Logic and Metaphysics Workshop
Date: Monday, November 21, 4.15-6.15 (NY time), GC 7314

Marko Malink (NYU) and Anubav Vasudevan (University of Chicago).
Title: The origins of conditional logic: Theophrastus on hypothetical syllogisms

Abstract: Łukasiewicz maintained that “the first system of propositional logic was invented about half a century after Aristotle: it was the logic of the Stoics”. In this talk, we argue that the first system of propositional logic was, in fact, developed by Aristotle’s pupil Theophrastus. Theophrastus sought to establish the priority of categorical over propositional logic by reducing various modes of propositional reasoning to categorical form. To this end, he interpreted the conditional “If φ then ψ” as a categorical proposition “A holds of all B”, in which B corresponds to the antecedent φ, and A to the consequent ψ. Under this interpretation, Aristotle’s law of subalternation (A holds of all B, therefore A holds of some B) corresponds to a version of Boethius’ Thesis (If φ then ψ, therefore not: If φ then not-ψ). Jonathan Barnes has argued that this consequence renders Theophrastus’ program of reducing propositional to categorical logic inconsistent. In this paper, we show that Barnes’s objection is inconclusive. We argue that the system developed by Theophrastus is both non-trivial and consistent, and that the propositional logic generated by Theophrastus’ system is exactly the connexive variant of the first-degree fragment of intensional linear logic.

Rutgers Logic Seminar
Monday, November 21, 5pm, Rutgers University, Hill 705
This specially scheduled seminar will be held at 5pm in order not to clash with the Wales vs USA World Cup match.
Simon Thomas, Rutgers
Invariant Random Subgroups and Characters

- - - - Tuesday, Nov 22, 2022 - - - -

Models of Peano Arithmetic (MOPA)
Tuesday, November 22, 1:00pm
Virtual (email Victoria Gitman vgitman@nylogic.org for meeting id)

Joel David Hamkins, University of Notre Dame
Pointwise definable and Leibnizian extensions of models of arithmetic and set theory

I shall introduce a flexible new method showing that every countable model of PA admits a pointwise definable end-extension, one in which every individual is definable without parameters. And similarly for models of set theory, in which one may also achieve the Barwise extension result—every countable model of ZF admits a pointwise definable end-extension to a model of ZFC+V=L, or indeed any theory arising in a suitable inner model. A generalization of the method shows that every model of arithmetic of size at most continuum admits a Leibnizian extension, and similarly in set theory.

Computational Logic Seminar
Fall Semester 2022
Tuesday, November 22
Time 2:00 - 4:00 PM

Room 3310-B,
The talk will be delivered online for a live audience,
for a zoom link contact SArtemov@gmail.com

SpeakerNeil De Boer, The Ohio State University
Title: Justification Logic and Type Theory as Formalizations of Intuitionistic Propositional Logic
Abstract:
We explore two ways of formalizing Kreisel's addendum to the Brouwer-Heyting-Kolmogorov interpretation. To do this we compare Artemov's justification logic with simply typed $\lambda$ calculus. First, we provide a completeness result for Kripke-style semantics of the implicational fragment of the intuitionistic logic of proofs. Then we introduce a map from justification terms into $\lambda$ terms, which can be viewed as a method of extracting the computational content of the justification terms. Then we examine the interpretation of Kreisel's addendum in justification logic along with the image of the resulting justification terms under our map.

- - - - Wednesday, Nov 23, 2022 - - - -

The New York City Category Theory Seminar
Department of Computer Science
Department of Mathematics
The Graduate Center of The City University of New York

Speaker:     Saeed Salehi, University of Tabriz.

Date and Time:     Wednesday November 23, 2022, Zoom Talk SPECIAL TIME 9:30AM-11:00AM.

Title:     Self-Reference and Diagonalization: their difference and a short history.

Abstract: What is now called the Diagonal (or the Self-Reference) Lemma, is the statement that for every formula F(x), with the only free variable x, there exists a sentence σ such that σ is equivalent to the F of the Gödel code of σ, i.e., σ  F(#σ); and this equivalence is provable in certain weak arithmetics. This lemma is credited to Gödel (1931), in the special case when F is the unprovability predicate, and to Carnap (1934) in the more general case.

In this talk, we will argue that Gödel-Carnap's original Diagonal Lemma is not the modern formulation and was more similar to, but not exactly identical with, the Strong Diagonal (or Direct Self-Reference) Lemma. This lemma, so-called recently, says that for every formula F(x), in a sufficiently expressive language, there exists a sentence σ such that σ is equal to the F of the Gödel code of σ, i.e., σ = F(#σ); and this equality is provable in sufficiently strong theories. We will attempt at tracking down the first appearance of the modern formulation of the Diagonal Lemma in the equivalent form, also in the strong direct form of equality.

- - - - Thursday, Nov 24, 2022 - - - -

*** Thanksgiving Day ***

- - - - Friday, Nov 25, 2022 - - - -

Next Week in Logic at CUNY:

- - - - Monday, Nov 28, 2022 - - - -

Logic and Metaphysics Workshop
Date: Monday, November 28, 4.15-6.15 (NY time), GC 7314
William McCarthy (Columbia).

Title: Modal pluralism and higher-order logic

Abstract: Modal pluralism is the view that there are a variety of candidate interpretations of the predicate ‘could have been the case that’ which give intuitively different answers to paradigmatic metaphysical questions (‘intuitively’ because the phrase means subtly different things on the different interpretations). It is the modal analog of set-theoretic pluralism, according to which there are a variety of candidate interpretations of ‘is a member of’.  Of course, if there were a broadest kind of counterfactual possibility, then one could define every other kind as a restriction on it, as in the set-theoretic case.  It would then be privileged in the way that a broadest kind of set would be, if there were one.  Recently, several authors have purported to prove from higher-order logical principles that there is a broadest kind of possibility. In this talk we critically assess these arguments.  We argue that they rest on an assumption which any modal pluralist should reject: namely, monism about higher-order logic. The reasons to be a modal pluralist are also reasons to be a pluralist about higher-order quantification. But from the pluralist perspective on higher-order logic, the claim that there is a broadest kind of possibility is like the Continuum Hypothesis, according to the set-theoretic pluralist.  It is true on some interpretations of the relevant terminology, and false on others.  Consequently, the significance of the ‘proof’ that there is a broadest kind of possibility is deflated.  Time permitting, we will conclude with some upshots of higher-order pluralism for the methodology of metaphysics.

Note: This is joint work with Justin Clarke-Doane.

- - - - Tuesday, Nov 29, 2022 - - - -

- - - - Wednesday, Nov 30, 2022 - - - -

The New York City Category Theory Seminar
Department of Computer Science
Department of Mathematics
The Graduate Center of The City University of New York
Date and Time:     Wednesday November 30, 2022, 7:00 - 8:30 PM.
TBA

- - - - Thursday, Dec 1, 2022 - - - -

- - - - Friday, Dec 2, 2022 - - - -

Set Theory Seminar
CUNY Graduate Center, Friday, December 2, 12:15pm NY time
Virtual: Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Michał Tomasz Godziszewski University of Vienna

Logic Workshop
Hybrid: Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Friday December 2, 2:00pm-3:30pm, Room 6417
Will Boney Texas State University

- - - - Other Logic News - - - -

- - - - Web Site - - - -

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

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

## Wednesday seminar

Prague Set Theory Seminar
Dear all, The seminar meets on Wednesday November 23th at 11:00 in the Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building. Program: Sarka Stejskalova -- Automorphisms of trees In the talk we will focus on omega_1-trees. We will discuss the number of nontrivial automorphisms which can exist on a given omega_1-tree. We will also discuss how to add an automorphism to an omega_1-tree with a well-behaved forcing, and we will identify some restrictions for these forcings (for instance, they cannot be sigma-closed for Suslin trees). In the last part of the talk, we will mention some open questions regarding automorphisms of omega_1-trees. Best, David

## (KGRC) guests, video recordings, seminar talks Tuesday, November 22 and Thursday, November 24

Kurt Godel Research Center
Martin Hils (host: Matthias Aschenbrenner) visits the KGRC until March 31, 2023 and gives a talk on January 19, 2023 (details to be announced at a later time). Franz-Viktor Kuhlmann (host: Matthias Aschenbrenner) visits the KGRC until January 31, 2023 and gives a talk on November 24 (see below). David Chodounsky (host: Vera Fischer) visits the KGRC from December 4 until December 8 and gives a talk on December 6 (details to be announced at a later time). Jan Hubicka (host: Vera Fischer) visits the KGRC from December 5 until December 8 and gives a talk on December 6 (details to be announced at a later time). Stefan Ludwig (hosts: Martin Hils and Matthias Aschenbrenner) visits the KGRC from December 5 to December 14. * * * For some recent seminar talks, video recordings are available: "Entire functions and the continuum" by Jonathan Schilhan on November 10: https://univienna.zoom.us/rec/share/WLqHDNlpF4W__jPMOIXe-OvnibgGCCP3ukttxkfh4MIIHoCUC0q6A69vI_ch6jwY.HImCMpOEXxs60rf3 (passcode t0z4?muN) "Compactness versus hugeness at successor cardinals, part 2" by Monroe Eskew on November 15: https://univienna.zoom.us/rec/share/ciurhrPPdzEQHrCS6ro11bEZ4LPuhKJ5bNGzIcBgSqCsr_NrIGHp2-8U_RiJHIsK.bj-YKnjNACDK1Q4e (passcode f9xDpS&&) "The Axiom of Choice and large cardinals" by Farmer Schlutzenberg on November 17: https://univienna.zoom.us/rec/share/zlY9CldOLrKfL7R1rIZTZ21MW8YLrk0mRRvXykIWPLU0fpkdPxmguYX7cjH2RCqJ.17d3feAKcAZWTTWu (passcode wR^81nq7) * * * Set Theory Research Seminar Kurt Gödel Research Center Tuesday, November 22 "Subversion Forcing, part 1" Corey Switzer (KGRC) In these two talks we will introduce Jensen's classes of subcomplete and subproper forcing as well as discuss some applications due to the speaker and Fuchs, and the speaker and Sakai. An important feature of proper forcing is the countable covering property: every countable set of ordinals added by a proper forcing notion is contained in a ground model countable set of ordinals. This is important in iteration theorems. Subproper forcing is a weakening of proper forcing that is still iterable while including some well known forcing notions which do add countable sets of ordinals that are not covered by anything in the ground model including Namba forcing (under CH) and Prikry forcing. One can weaken other classes of forcing notions in a similar way and the "sub"version of the countably closed forcing, known as subcomplete forcing, is a particularly interesting subclass of subproper forcing that was used by Jensen in several applications including his solution to the extended Namba problem. In the first of these talks I will introduce the classes subproper and subcomplete forcing as well as discuss simplifications of them due to Fuchs and myself. Time permitting I will discuss new iterations theorems for these classes reminiscent of similar theorems proved for proper forcing in the context of the reals and combinatorics on $\omega_1$ ($\omega^\omega$-bounding, preservation of Souslin trees etc). In the second talk I will discuss the forcing axioms for these classes including their applications and limitations. In particular, time permitting, I will discuss a recent result, joint with Hiroshi Sakai that the forcing axiom for subcomplete forcing is compatible with a $\square_{\omega_1}$-sequence. The take away is a class of strong forcing axioms that are compatible with a wide variety of behaviour on the level of the reals and combinatorics on cardinals below the continuum. Time and Place Talk at 3:00pm in hybrid mode, in person as well as via Zoom. (Students at Uni Wien are required to attend in person.) Universität Wien Institut für Mathematik Kolingasse 14-16 1090 Wien 1st floor Seminar room 10 For details about how to join the Zoom session, please see the end of this message. * * * Logic Colloquium Kurt Gödel Research Center Thursday, November 24 "Nonstandard models of the reals and symmetrical completeness" Franz-Viktor Kuhlmann (University of Szczecin, PL) The notion of power series fields provides an easy method for the construction of nonstandard models of the ordered field of real numbers. I will define them, as well as Hahn products, which are their equivalent in the case of ordered abelian groups. The question arises whether these power series models can also have additional structures or properties that we know from the reals. For example, it was shown in joint work with Salma Kuhlmann and Saharon Shelah that they do not admit exponential functions which have the same elementary properties as the exponential function on the reals. In a different direction, the question came up whether they could support generalizations of Banach’s Fixed Point Theorem. I will introduce the notions of symmetrically complete ordered fields, abelian groups and sets and characterize those power series models of the reals that are symmetrically complete. They indeed admit a (nonarchimedean) generalization of Banach’s Fixed Point Theorem. Their construction is the result of joint work with Katarzyna Kuhlmann and Saharon Shelah. It heavily relies on the analysis of cuts in ordered power series fields and Hahn products. Time and Place Talk at 3:00pm in hybrid mode, in person as well as via Zoom. (Students at Uni Wien are required to attend in person.) Universität Wien Institut für Mathematik Kolingasse 14-16 1090 Wien 1st floor Seminar room 10 Zoom for both talks: If you need the Zoom data and have not received the meeting link by the day before the talk, please contact richard.springer@univie.ac.at! (Please direct any other requests about the seminars and Zoom meeting(s) to vera.fischer@univie.ac.at.)

## Barcelona Set Theory Seminar

Barcelona Logic Seminar

Dear All,
Please find attached the announcement of the next Barcelona Set Theory Seminar session.

SPEAKER:  Jiachen Yuan
TITLE: On the cofinality of the least omega_1-strongly compact cardinal
DATE: Wednesday, 23 November 2022
TIME: 16:00 (CET)
PLACE: Room B1 (UB). The Seminar can also be followed online via Zoom:

Best regards,
Joan

P.S.: If you do not wish to receive any more announcements, please send an email to bagaria@ub.edu with the text “Unsubscribe”.

Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia

Phone: +34 93 402 1609
joan.bagaria@icrea.cat
bagaria@ub.edu

## Nankai Logic Colloquium

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 Menachem Shlossberg from Reichman University. This talk is going to take place this Friday,  Nov. 18 2022,  from 4 pm to 5 pm (UTC+8, Beijing time).

Title: Minimality conditions equivalent  to  the finitude of Fermat  and Mersenne primes.

Abstract: It is still open whether there exist infinitely many Fermat primes or
infinitely many composite Fermat numbers. The same question concerning the
Mersenne numbers is also unsolved. Extending some results from [1], we characterize
the Fermat primes and the Mersenne primes in terms of topological minimality of
some matrix groups. This is done by showing, among other things, that if F is a
subfield of a local field of characteristic distinct than 2, then the special upper triangular group ST+(n, F) is minimal precisely when the special linear group SL(n, F) is. We provide criteria for the minimality (and total minimality) of SL(n, F) and ST+(n, F), where F is a subfield of C.
Let  $\mathcal F_\pi$ and  $\mathcal F_c$   be the set of Fermat primes and the set of composite Fermat numbers, respectively.
As our main result, we prove that the following conditions
are equivalent for $\mathcal A \in {\mathcal F_\pi, \mathcal F_c} :$
•  $\mathcal A$  is finite;
• $\prod_{F_n\in \mathcal A} SL(Fn −1,Q(i))$ is minimal, where Q(i) is the Gaussian rational field;
•  $\prod_{F_n\in \mathcal A} ST+(Fn − 1,Q(i))$ is minimal.

Similarly, denote by  $\mathcal M_\pi$ and  $\mathcal M_c$  the set of Mersenne primes and the set of composite
Mersenne numbers, respectively, and let $\mathcal B \in {\mathcal M_\pi, \mathcal M_c}$. Then the following
conditions are equivalent:
• $\mathcal B$  is finite;
• $\prod_{M_p\in \mathcal B} SL(M_p + 1,Q(i))$ is minimal;
• $\prod_{M_p\in \mathcal B} ST+(M_p + 1,Q(i))$ is minimal.

[1] M. Megrelishvili, M. Shlossberg, Minimality of topological matrix groups and Fermat primes, Topol. Appl. 322(2022), doi:10.1016/j.topol.2022.108272.
___________________________________________________________________________________________________________________________________________________

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

Title：                 The 10th Nankai Logic Colloquium -- Menachem Shlossberg

Time：                16:00pm, Nov. 18, 2022 (Beijing Time)

Zoom Number：850 1491 3444

Passcode：         596956

_____________________________________________________________________

Best wishes,

Ming Xiao

## Cross-Alps Logic Seminar (speaker: Annalisa Conversano)

Cross-Alps Logic Seminar
On Friday 18.11.2022 at 9:00
Annalisa Conversano (University of Genoa)
will give a talk on
Tools of o-minimality in the study of groups

Please refer to the usual webpage of our LogicGroup for more details and the abstract of the talk.
The seminar will be held remotely through Webex. Please write to 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 2017 'Mathematical logic: models, sets, computability'.

## This Week in Logic at CUNY

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

- - - - Monday, Nov 14, 2022 - - - -

Rutgers Logic Seminar
Monday, November 14, 3:30pm, Rutgers University, Hill 705
Sumun Iyer, Cornell
Dynamics of the Knaster continuum homeomorphism group

Logic and Metaphysics Workshop
Date: Monday, November 14, 4.15-6.15 (NY time), GC 7315
Christopher Izgin (Humboldt University).
Title: A new approach to Aristotle’s definitions of truth and falsehood in Metaphysics Γ.7

Abstract: At Metaphysics Γ.7, 1011b26–7, Aristotle defines truth and falsehood as follows: to assert of what is that it is or of what is not that it is not, is true; to assert of what is that it is not or of what is not that it is, is false. In their attempts to interpret the definitions, scholars usually distinguish between the veridical, 1-place, and 2-place uses of ‘to be’. The dominant view holds that all occurrences of ‘is’ in the definientia are interpreted veridically (Kahn 1966, Kirwan 1993, Crivelli 2004, Kimhi 2018, Szaif 2018). So the first truth condition is interpreted as follows: to assert of what is the case that it is the case, is true. I argue against this and side with those who favor a comprehensive—i.e. a jointly 1- and 2-place—interpretation (Matthen 1983, Wheeler 2011), according to which the first truth condition says: to assert of what is (F, exists) that it is (F, exists), is true. It is an open question how this interpretation makes Aristotle’s definitions sufficiently general so as to accommodate all propositional truth-value bearers. I first show that all Aristotelian propositions are reducible to propositions involving a 1- or 2-place ‘is’ and that formal properties, such as quantity and modality, merely modify the ‘is’, thus lending support to the comprehensive interpretation.

- - - - Tuesday, Nov 15, 2022 - - - -

Models of Peano Arithmetic (MOPA)
Tuesday, November 15, 7:00pm
Virtual (email Victoria Gitman vgitman@nylogic.org for meeting id)
Roman Kossak, CUNY
Generalized quantifiers in arithmetic II

This will be another talk in the MOPA series on the history of the subject.

The work on generalized quantifiers in formal systems of arithmetic was initiated in 1980 by Macintyre, motivated by the search for natural extensions of first-order arithmetic that are immune to the Kirby-Paris-Harrington style independence results. Some open questions posed by Macintyre were solved in a definitive way in 1982 by Schmerl and Simpson and after that Schmerl wrote two more papers on for Peano Arithmetic in the languages with Ramsay stationary quantifiers. Some results of Macintyre were obtained independently by Carl Morgenstern. All these papers, while very well written, are quite technical and not easily accessible for readers who are not familiar with more advanced tools of the model theory of arithmetic. I will survey the results suppressing most technical details. I will also talk about an attempt to use logic with stationary quantifiers to classify -like recursively saturated models of PA.

- - - - Wednesday, Nov 16, 2022 - - - -

- - - - Thursday, Nov 17, 2022 - - - -

- - - - Friday, Nov 18, 2022 - - - -

Set Theory Seminar
CUNY Graduate Center, Friday, November 18, 12:15pm NY time
Virtual: Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Brent Cody Virginia Commonwealth University

Sparse analytic systems

Given a set , an -predictor  is a function that takes as inputs functions of the form , where , and outputs a guess  for what  'should be.' An -predictor is good if for all total functions  the set of  for which the guess  is not equal to  has measure zero. Hardin and Taylor proved that every set  has a good -predictor and they raised various questions asking about the extent to which the prediction  made by a good predictor might be invariant after precomposing  with various well-behaved functions - this leads to the notion of 'anonymity' of good predictors under various classes of functions. Bajpai and Velleman answered several of Hardin and Taylor's questions and asked: Does there exist, for every set , a good -predictor that is anonymous with respect to the strictly increasing analytic homeomorphisms of ? We provide a consistently negative answer to this question by strengthening a result of Erdős, which states that the Continuum Hypothesis is equivalent to the existence of an uncountable family  of (real or complex) analytic functions, such that  is countable for every . We strengthen Erdős' result by proving that CH is equivalent to the existence of what we call sparse analytic systems of functions. This is joint work with Sean Cox and Kayla Lee.

Logic Workshop
Hybrid: Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Friday November 18, 2:00pm-3:30pm, Room 6417

Dima Sinapova Rutgers University

Dima Sinapova, Rutgers University
Prikry sequences and square properties at

It is well known that if an inaccessible cardinal  is singularized to countable cofinality while preserving cardinals, then  holds in the outer model. Moreover, this remains true even when relaxing the cardinal preservation assumption a bit. In this talk we focus on when Prikry forcing adds weaker forms of square in a more general setting. We prove abstract theorems about when Prikry forcing with interleaved collapses to bring down the singularized cardinal to  will add a weak square sequence. This can be viewed as a partial positive result to a question of Woodin about whether the failure of SCH at  implies weak square.

Next Week in Logic at CUNY:

- - - - Monday, Nov 21, 2022 - - - -

Logic and Metaphysics Workshop
Date: Monday, November 21, 4.15-6.15 (NY time), GC 7315

Marko Malink (NYU) and Anubav Vasudevan (University of Chicago).
Title: The origins of conditional logic: Theophrastus on hypothetical syllogisms

Abstract: Łukasiewicz maintained that “the first system of propositional logic was invented about half a century after Aristotle: it was the logic of the Stoics”. In this talk, we argue that the first system of propositional logic was, in fact, developed by Aristotle’s pupil Theophrastus. Theophrastus sought to establish the priority of categorical over propositional logic by reducing various modes of propositional reasoning to categorical form. To this end, he interpreted the conditional “If φ then ψ” as a categorical proposition “A holds of all B”, in which B corresponds to the antecedent φ, and A to the consequent ψ. Under this interpretation, Aristotle’s law of subalternation (A holds of all B, therefore A holds of some B) corresponds to a version of Boethius’ Thesis (If φ then ψ, therefore not: If φ then not-ψ). Jonathan Barnes has argued that this consequence renders Theophrastus’ program of reducing propositional to categorical logic inconsistent. In this paper, we show that Barnes’s objection is inconclusive. We argue that the system developed by Theophrastus is both non-trivial and consistent, and that the propositional logic generated by Theophrastus’ system is exactly the connexive variant of the first-degree fragment of intensional linear logic.

- - - - Tuesday, Nov 22, 2022 - - - -

Models of Peano Arithmetic (MOPA)
Tuesday, November 22, 7:00pm
Virtual (email Victoria Gitman vgitman@nylogic.org for meeting id)

Joel David Hamkins, University of Notre Dame
Pointwise definable and Leibnizian extensions of models of arithmetic and set theory

I shall introduce a flexible new method showing that every countable model of PA admits a pointwise definable end-extension, one in which every individual is definable without parameters. And similarly for models of set theory, in which one may also achieve the Barwise extension result—every countable model of ZF admits a pointwise definable end-extension to a model of ZFC+V=L, or indeed any theory arising in a suitable inner model. A generalization of the method shows that every model of arithmetic of size at most continuum admits a Leibnizian extension, and similarly in set theory.

- - - - Wednesday, Nov 23, 2022 - - - -

The New York City Category Theory Seminar
Department of Computer Science
Department of Mathematics
The Graduate Center of The City University of New York, Room 6417

Speaker:     Saeed Salehi, University of Tabriz.

Date and Time:     Wednesday November 23, 2022, TIME TBA.

Title:     Self-Reference and Diagonalization: their difference and a short history.

Abstract: What is now called the Diagonal (or the Self-Reference) Lemma, is the statement that for every formula F(x), with the only free variable x, there exists a sentence σ such that σ is equivalent to the F of the Gödel code of σ, i.e., σ  F(#σ); and this equivalence is provable in certain weak arithmetics. This lemma is credited to Gödel (1931), in the special case when F is the unprovability predicate, and to Carnap (1934) in the more general case.

In this talk, we will argue that Gödel-Carnap's original Diagonal Lemma is not the modern formulation and was more similar to, but not exactly identical with, the Strong Diagonal (or Direct Self-Reference) Lemma. This lemma, so-called recently, says that for every formula F(x), in a sufficiently expressive language, there exists a sentence σ such that σ is equal to the F of the Gödel code of σ, i.e., σ = F(#σ); and this equality is provable in sufficiently strong theories. We will attempt at tracking down the first appearance of the modern formulation of the Diagonal Lemma in the equivalent form, also in the strong direct form of equality.

- - - - Thursday, Nov 24, 2022 - - - -

- - - - Friday, Nov 25, 2022 - - - -

- - - - Other Logic News - - - -

- - - - Web Site - - - -

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

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

## Wednesday seminar

Prague Set Theory Seminar
Dear all, The seminar meets on Wednesday November 16th at 11:00 in the Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building. Program: David Uhrik -- Characterizing Uncountable Trees using Graphs I will prove a connection between the uncountable Hadwiger conjecture and non-special trees. Also characterizations of Aronszajn, Kurepa and Suslin trees using graphs will be deduced. Best, David

## Upcoming Core Model Seminar

Carnegie Mellon Logic Seminar
TUESDAY, November 15, 2022 Core Model Seminar: 1:30 to 3 PM Eastern, Online, Sandra Müller, TU Wien Join Zoom Meeting: https://cmu.zoom.us/j/97749733438?pwd=Yk5PcSsvekptWWxMNUhCU2pFbzA0Zz09 Meeting ID: 977 4973 3438 Passcode: 457791 TITLE: A stationary-tower-free proof of Sealing, part 2 ORGANIZERS' NOTE: The recording and presentation materials from part 1 are available in our archive. Please email us to request access. ABSTRACT: Sealing is a generic absoluteness principle for the theory of the universally Baire sets of reals introduced by Woodin. It is deeply connected to the Inner Model Program and plays a prominent role in recent advances in inner model theory. Woodin showed in his famous Sealing Theorem that in the presence of a proper class of Woodin cardinals Sealing holds after collapsing a supercompact cardinal. In the first talk, I will outline the importance of Sealing and discuss a new and stationary-tower-free proof of Woodin’s Sealing Theorem that is based on Sargsyan’s and Trang’s proof of Sealing from iterability. In the second talk, I will outline the proof of an extension of the SealingTheorem that gives models in which Theta is regular. This is joint work with Grigor Sargsyan.

## Barcelona Set Theory Seminar

Barcelona Logic Seminar
Dear All,
Please find attached the announcement of the next Barcelona Set Theory Seminar session.

SPEAKER: Jeffrey Bergfalk
TITLE: The definable content of homological invariants
DATE: Wednesday, 16 November 2022
TIME: 16:00 (CET)
PLACE: Room B1 (UB). The Seminar can also be followed online via Zoom:

Best regards,
Joan

P.S.: If you do not wish to receive any more announcements, please send an email to bagaria@ub.edu with the text “Unsubscribe”.

Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia

Phone: +34 93 402 1609
joan.bagaria@icrea.cat
bagaria@ub.edu

## Talk by Cristian Calude at CQT on 16 Nov 2022 16:00 hrs

NUS Logic Seminar
The following seminar is held by Cristian Calude who works in Algorithmic Randomness as well as in Quantum Computing. Speaker: Cristian Calude Date: Wednesday 16 November 2022 at 16:00 hrs Location: Centre for Quantum Technologies, Seminar Room L3, S15#03-15, NUS Also as Zoom Meeting: https://nus-sg.zoom.us/j/2817341692 Title: Photonic Ternary Quantum Random Number Generators Abstract: We construct a class of 3-dimensional photonic quantum random number generators and prove that each generates maximally unpredictable digits via measurements that are robust to errors. In particular, every sequence generated is strongly incomputable; hence its quality is provable better than that of every pseudo-random sequence. We also briefly contrast 2-dimensional and 3-dimensional quantum random number generators, discuss photonic implementations and show the superiority of the latter ones. These results suggest that incomputability in physics is real and practically useful.

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

Kurt Godel Research Center
The KGRC welcomes as guests: Martin Hils (host: Matthias Aschenbrenner) visits the KGRC until March 31, 2023 and gives a talk on January 19, 2023 (details to be announced at a later time). Jonathan Schilhan (host: Thilo Weinert) visits the KGRC until November 15. Franz-Viktor Kuhlmann (host: Matthias Aschenbrenner) visits the KGRC from November 15 until January 31, 2023 and gives a talk on November 24 (details to be announced at a later time). David Chodounsky (host: Vera Fischer) visits the KGRC from December 4 until December 8 and gives a talk on December 6 (details to be announced at a later time). Jan Hubicka (host: Vera Fischer) visits the KGRC from December 5 until December 8 and gives a talk on December 6 (details to be announced at a later time). Stefan Ludwig (hosts: Martin Hils and Matthias Aschenbrenner) visits the KGRC from December 5 to December 14. * * * Set Theory Research Seminar Kurt Gödel Research Center Tuesday, November 15 "Compactness versus hugeness at successor cardinals, part 2" Monroe Eskew (KGRC) There are several ways in which small cardinals can behave like large ones. One variety is compactness phenomena, such as the tree property, which characterize when inaccessible cardinals satisfy some strong large cardinal notions, but can consistently hold at small cardinals such as $\omega_2$. Another variety is generic embedding properties coming from saturated ideals or Chang's Conjecture that resemble embeddings associated with huge cardinals. The known forcing strategies for obtaining compactness and hugeness properties at small cardinals are very different. Can they be made to hold simultaneously? In these talks, we present some combinatorial barriers to combining them, and we show why several forcing approaches will not work. Hopefully, by narrowing down the space of possibilities, these negative results will point towards a path to answering our question. Time and Place Talk at 3:00pm in hybrid mode, in person as well as via Zoom. (Students at Uni Wien are required to attend in person.) Universität Wien Institut für Mathematik Kolingasse 14-16 1090 Wien 1st floor Seminar room 10 For details about how to join the Zoom session, please see the end of this message. * * * Logic Colloquium Kurt Gödel Research Center Thursday, November 17 "The Axiom of Choice and large cardinals" Farmer Schlutzenberg (Universität Münster, DE) The Axiom of Choice (AC) is mostly accepted by mathematicians, and is essential in many proofs. However, it seems to be accepted with less confidence than the other axioms of set theory, probably due to its non-constructive nature and its various unexpected consequences. Large cardinals are central axioms in set theory, with compelling consequences for the universe of sets, not only for "large" sets but also for "small" ones like real numbers and sets thereof. It turns out that the relationship between AC and large cardinals is intricate, and not entirely without conflict. The connections might even be taken to suggest that the correct picture of the universe of sets is one in which very large cardinals exist and the full Axiom of Choice must fail. I will survey some of the recent work in this area. The talk will be aimed at a general logic audience. Time and Place Talk at 3:00pm in hybrid mode, in person as well as via Zoom. (Students at Uni Wien are required to attend in person.) Universität Wien Institut für Mathematik Kolingasse 14-16 1090 Wien 1st floor Seminar room 10 Zoom for both talks: If you need the Zoom data and have not received the meeting link by the day before the talk, please contact richard.springer@univie.ac.at! (Please direct any other requests about the seminars and Zoom meeting(s) to vera.fischer@univie.ac.at.)

## Nankai Logic Colloquium

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 Cesar E. Silva from William College. This talk is going to take place this Friday, Nov 11, 2022,  from 9 am to 10 am(UTC+8, Beijing time).

Title: On examples and properties of notions of weak mixing for nonsingular transformations

Abstract: This will largely be a survey talk on several notions of the weak mixing property for nosingular and infinite measure preserving transformations. There are several interesting and seemingly different properties of the weak mixing property that all happen to be equivalent in the case of finite measure preserving transformations. Since the early work of Kakutani and Parry (1963) it has been know that not all these notions are equivalent in the case of infinite measure preserving transformations. We will discuss several of these notions, their implications and counter examples, including some recent work, and topological models for these transformations.

___________________________________________________________________________________________________________________________________________________

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

Title：                 The 9th Nankai Logic Colloquium -- Cesar E. Silva

Time：                9:00am, nov. 11, 2022 (Beijing Time)

Zoom Number：825 9529 2118

Passcode：         475473

_____________________________________________________________________

Best wishes,

Ming Xiao

## This Week in Logic at CUNY

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

- - - - Monday, Nov 7, 2022 - - - -

Rutgers Logic Seminar
Monday, November 7, 3:30pm, Rutgers University, Hill 705
Simon Thomas, Rutgers University
Invariant random subgroups and characters
Nov 7th, Tom Benhamou, UIC

Logic and Metaphysics Workshop
Date: Monday, November 7, 4.15-6.15 (NY time), GC 7315

Victoria Gitman (CUNY).
Title: Set theory without the powerset axiom

Abstract: Many natural and useful set-theoretic structures fail to satisfy the Powerset axiom. For example, the universe of sets can be decomposed into the H_alpha-hierarchy, indexed by cardinals alpha, where each H_alpha consists of all sets whose transitive closure has size less than alpha. If alpha is a regular cardinal, then H_alpha satisfies all axioms of ZFC except, maybe, the Powerset axiom (it will only satisfy Powerset if alpha is inaccessible). Class forcing extensions of models of ZFC will often fail to satisfy ZFC, but if the class forcing is nice enough, then it will preserve all the axioms of ZFC except, maybe, the Powerset axiom. Finally, a strong second-order set theory, extending Kelley-Morse by adding a choice principle for classes (Choice Scheme), is bi-interpretable with a strong first-order set theory without the Powerset axiom. Thus working in a strong enough second-order set theory can be reinterpreted as working in a strong first-order set theory in which the Powerset axiom fails. It turns out that simply taking the axioms of ZFC and removing the Powerset axiom does not yield a robust set theory. I will discuss robust (and strong) axiomatizations of set theory without Powerset and how much of the standard set theoretic machinery is still effective even in the strongest theories in the absence of Powerset. Because of the bi-interpretability of a strong set theory without Powerset with Kelley-Morse plus Choice Scheme, these results will have consequences for which set theoretic machinery continues to work in set theories with classes. Time permitting, I will also talk about some unexpectedly strange models of set theory without Powerset.

- - - - Tuesday, Nov 8, 2022 - - - -

Computational Logic Seminar
Fall Semester 2022, Tuesday, November 8, Time 2:00 - 4:00 PM, Room 3310-B
Speaker: Eoin Moore, Graduate Center CUNY
Title:  Soundness and completeness results for LEA and probability semantics

Abstract: The goal of the logic of evidence aggregation (LEA) was to describe probabilistic evidence aggregation in the setting of formal logic. However, as noted in that paper, LEA is not complete with respect to probability semantics. This leaves open the tasks to find sound and complete semantics for LEA and a proper axiomatization for probability semantics. We do both. We define a class of basic models called deductive basic models, and show LEA is sound and complete with respect to this class. On the other side, we define an axiomatic system LEA+ extending LEA and show it is sound and complete with respect to probability semantics. Close connections to Propositional Lax Logic are also demonstrated.

Models of Peano Arithmetic (MOPA)
Tuesday, November 8, 7:00pm
Virtual (email Victoria Gitman vgitman@nylogic.org for meeting id)
Roman Kossak, CUNY
Generalized quantifiers in arithmetic

This will be another talk in the MOPA series on the history of the subject.

The work on generalized quantifiers in formal systems of arithmetic was initiated in 1980 by Macintyre, motivated by the search for natural extensions of first-order arithmetic that are immune to the Kirby-Paris-Harrington style independence results. Some open questions posed by Macintyre were solved in a definitive way in 1982 by Schmerl and Simpson and after that Schmerl wrote two more papers on for Peano Arithmetic in the languages with Ramsay stationary quantifiers. Some results of Macintyre were obtained independently by Carl Morgenstern. All these papers, while very well written, are quite technical and not easily accessible for readers who are not familiar with more advanced tools of the model theory of arithmetic. I will survey the results suppressing most technical details. I will also talk about an attempt to use logic with stationary quantifiers to classify -like recursively saturated models of PA.

- - - - Wednesday, Nov 9, 2022 - - - -

The New York City Category Theory Seminar
Department of Computer Science
Department of Mathematics
The Graduate Center of The City University of New York, Room 6417

Speaker:     Andrei Rodin, University of Lorraine (Nancy, France).

Date and Time:     Wednesday November 9, 2022, 7:00 - 8:30 PM.

Title:     Kolmogorov's Calculus of Problems and Homotopy Type theory.

Abstract: A. N. Kolmogorov in 1932 proposed an original version of mathematical intuitionism where the concept of problem plays a central role, and which differs in its content from the versions of intuitionism developed by A. Heyting and other followers of L. Brouwer. The popular BHK-semantics of Intuitionistic logic follows Heyting's line and conceals the original features of Kolmogorov's logical ideas. Homotopy Type theory (HoTT) implies a formal distinction between sentences and higher-order constructions and thus provides a mathematical argument in favour of Kolmogorov's approach and against Heyting's approach. At the same time HoTT does not support the constructive notion of negation applicable to general problems, which is informally discussed by Kolmogorov in the same context. Formalisation of Kolmogorov-style constructive negation remains an interesting open problem.

- - - - Thursday, Nov 10, 2022 - - - -

- - - - Friday, Nov 11, 2022 - - - -

Set Theory Seminar
Friday, November 11, 12:15pm NY time
Virtual: Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Peter Holy, Technical University of Vienna

Asymmetric Cut and Choose Games

We consider the following two player game of infinite length: We are given a starting set X, and the players go by the names 'Cut' and 'Choose'. They take turns making moves, and in each step, Cut partitions a given set into two disjoint pieces, starting from the set X in their first move, and then Choose gets to pick one of the pieces, which is then partitioned into two pieces by Cut in their next move etc. In the end, Choose wins in case the intersection of all of their choices has at least two (distinct) elements.

We will investigate some of the properties of this game — in particular, we will discuss some classic results on when it is possible for one of the players to have a strategy for winning the game. We will then continue to discuss some variations of this game and their relevance to set theory — many central set theoretic notions, such as certain large cardinal properties, notions of distributivity, precipitousness and strategic closure were either known or turned out to be closely connected and often equivalent to the (non-)existence of winning strategies in certain cut and choose games.

This is joint work with Philipp Schlicht, Christopher Turner and Philip Welch (all University of Bristol).

Logic Workshop
(There will be no Logic Workshop seminar today)

Next Week in Logic at CUNY:

- - - - Monday, Nov 14, 2022 - - - -

Rutgers Logic Seminar
Monday, November 14, 3:30pm, Rutgers University, Hill 705
Sumun Iyer, Cornell
Dynamics of the Knaster continuum homeomorphism group

Logic and Metaphysics Workshop
Date: Monday, November 14, 4.15-6.15 (NY time), GC 7315
Christopher Izgin (Humboldt University).
Title: A new approach to Aristotle’s definitions of truth and falsehood in Metaphysics Γ.7

Abstract: At Metaphysics Γ.7, 1011b26–7, Aristotle defines truth and falsehood as follows: to assert of what is that it is or of what is not that it is not, is true; to assert of what is that it is not or of what is not that it is, is false. In their attempts to interpret the definitions, scholars usually distinguish between the veridical, 1-place, and 2-place uses of ‘to be’. The dominant view holds that all occurrences of ‘is’ in the definientia are interpreted veridically (Kahn 1966, Kirwan 1993, Crivelli 2004, Kimhi 2018, Szaif 2018). So the first truth condition is interpreted as follows: to assert of what is the case that it is the case, is true. I argue against this and side with those who favor a comprehensive—i.e. a jointly 1- and 2-place—interpretation (Matthen 1983, Wheeler 2011), according to which the first truth condition says: to assert of what is (F, exists) that it is (F, exists), is true. It is an open question how this interpretation makes Aristotle’s definitions sufficiently general so as to accommodate all propositional truth-value bearers. I first show that all Aristotelian propositions are reducible to propositions involving a 1- or 2-place ‘is’ and that formal properties, such as quantity and modality, merely modify the ‘is’, thus lending support to the comprehensive interpretation.

- - - - Tuesday, Nov 15, 2022 - - - -

Models of Peano Arithmetic (MOPA)
Tuesday, November 15, 7:00pm
Virtual (email Victoria Gitman vgitman@nylogic.org for meeting id)
Roman Kossak, CUNY
Generalized quantifiers in arithmetic II

This will be another talk in the MOPA series on the history of the subject.

The work on generalized quantifiers in formal systems of arithmetic was initiated in 1980 by Macintyre, motivated by the search for natural extensions of first-order arithmetic that are immune to the Kirby-Paris-Harrington style independence results. Some open questions posed by Macintyre were solved in a definitive way in 1982 by Schmerl and Simpson and after that Schmerl wrote two more papers on for Peano Arithmetic in the languages with Ramsay stationary quantifiers. Some results of Macintyre were obtained independently by Carl Morgenstern. All these papers, while very well written, are quite technical and not easily accessible for readers who are not familiar with more advanced tools of the model theory of arithmetic. I will survey the results suppressing most technical details. I will also talk about an attempt to use logic with stationary quantifiers to classify -like recursively saturated models of PA.

- - - - Wednesday, Nov 16, 2022 - - - -

- - - - Thursday, Nov 17, 2022 - - - -

- - - - Friday, Nov 18, 2022 - - - -

Set Theory Seminar
CUNY Graduate Center, Friday, November 18, 12:15pm NY time
Virtual: Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Brent Cody Virginia Commonwealth University

Logic Workshop
Hybrid: Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Friday November 18, 2:00pm-3:30pm, Room 6417

Dima Sinapova Rutgers University

- - - - Other Logic News - - - -

- - - - Web Site - - - -

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

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

## Wednesday seminar

Prague Set Theory Seminar
Dear all, The seminar meets on Wednesday November 9th at 11:00 in the Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building. Program: Jonathan Cancino Manriquez -- More on the combinatorics of dense subsets of the rationals We will review some results about cardinal invariants related to the combinatorics of dense subsets of the rationals, mostly focused on almost disjoint families of dense subsets of the rationals. In particular, we will prove a generalization of a theorem of J. Steprans by proving that some parametrized diamond principles imply that the almost disjointness number of the boolean algebra P(Q)/nwd is omega_1(excluding countable maximal antichains) as well as proving that the additivity of the meager ideal is a lower bound for such cardinal invariant. Best, David

## (KGRC) sminar talks Tuesday, November 8 and Thursday, November 10

Kurt Godel Research Center
The KGRC welcomes as guests: Martin Hils (host: Matthias Aschenbrenner) visits the KGRC until March 31, 2023 and gives a talk on January 19, 2023 (details to be announced at a later time). Will Brian (host: Vera Fischer) visits the KGRC until November 6. Simone Ramello (host: Martin Hils) visits the KGRC until November 8. Jonathan Schilhan (host: Thilo Weinert) visits the KGRC until November 15 and gives a talk on November 10 (see below). Franz-Viktor Kuhlmann (host: Matthias Aschenbrenner) visits the KGRC from November 15 until January 31, 2023 and gives a talk on November 24 (details to be announced at a later time). David Chodounsky (host: Vera Fischer) visits the KGRC from December 4 until December 8 and gives a talk on December 6 (details to be announced at a later time). Jan Hubicka (host: Vera Fischer) visits the KGRC from December 5 until December 8 and gives a talk on December 6 (details to be announced at a later time). Stefan Ludwig (hosts: Martin Hils and Matthias Aschenbrenner) visits the KGRC from December 5 to December 14. * * * Set Theory Research Seminar Kurt Gödel Research Center Tuesday, November 8 "Compactness versus hugeness at successor cardinals, part 1" Monroe Eskew (KGRC) There are several ways in which small cardinals can behave like large ones. One variety is compactness phenomena, such as the tree property, which characterize when inaccessible cardinals satisfy some strong large cardinal notions, but can consistently hold at small cardinals such as $\omega_2$. Another variety is generic embedding properties coming from saturated ideals or Chang's Conjecture that resemble embeddings associated with huge cardinals. The known forcing strategies for obtaining compactness and hugeness properties at small cardinals are very different. Can they be made to hold simultaneously? In these talks, we present some combinatorial barriers to combining them, and we show why several forcing approaches will not work. Hopefully, by narrowing down the space of possibilities, these negative results will point towards a path to answering our question. Time and Place Talk at 3:00pm in hybrid mode, in person as well as via Zoom. (Students at Uni Wien are required to attend in person.) Universität Wien Institut für Mathematik Kolingasse 14-16 1090 Wien 1st floor Seminar room 10 For details about how to join the Zoom session, please see the end of this message. * * * Logic Colloquium Kurt Gödel Research Center Thursday, November 10 "Entire functions and the continuum" Jonathan Schilhan (University of Leeds, GB) In the 60's, Erdős showed that the continuum hypothesis is equivalent to the statement that there is an uncountable family of entire functions on the complex plane that attains only countably many values at each point. The argument in fact shows that any family of entire functions, that attains at each point less values than elements of that family, must have size continuum. Recently Kumar and Shelah have shown that consistently such a family exists while the continuum has size $\aleph_{\omega_1}$. We answer their main open problem by showing that continuum $\aleph_2$ is possible as well. This is joint work with T. Weinert. Time and Place Talk at 3:00pm in hybrid mode, in person as well as via Zoom. (Students at Uni Wien are required to attend in person.) Universität Wien Institut für Mathematik Kolingasse 14-16 1090 Wien 1st floor Seminar room 10 Zoom for both talks: If you need the Zoom data and have not received the meeting link by the day before the talk, please contact richard.springer@univie.ac.at! (Please direct any other requests about the seminars and Zoom meeting(s) to vera.fischer@univie.ac.at.)

## Next Core Model Seminar

Carnegie Mellon Logic Seminar
TUESDAY, November 8, 2022 Core Model Seminar: 1:30 - 3 PM Eastern, Online, Sandra Müller, TU Wien Join Zoom Meeting: https://cmu.zoom.us/j/97749733438?pwd=Yk5PcSsvekptWWxMNUhCU2pFbzA0Zz09 Meeting ID: 977 4973 3438 Passcode: 457791 TITLE: A stationary-tower-free proof of Sealing, part 1 ABSTRACT: Sealing is a generic absoluteness principle for the theory of the universally Baire sets of reals introduced by Woodin. It is deeply connected to the Inner Model Program and plays a prominent role in recent advances in inner model theory. Woodin showed in his famous Sealing Theorem that in the presence of a proper class of Woodin cardinals Sealing holds after collapsing a supercompact cardinal. In the first talk, I will outline the importance of Sealing and discuss a new and stationary-tower-free proof of Woodin’s Sealing Theorem that is based on Sargsyan’s and Trang’s proof of Sealing from iterability. In the second talk, I will outline the proof of an extension of the Sealing Theorem that gives models in which Theta is regular. This is joint work with Grigor Sargsyan.

## Logic Seminar Wed 9 Nov 2022 17:00 hrs at NUS by Benjamin T Castle

NUS Logic Seminar
Invitation to the Logic Seminar at the National University of Singapore Date: Wednesday, 9 November 2022, 17:00 hrs Place: NUS, Department of Mathematics, S17#04-05 Speaker: Benjamin T Castle Title: Complex Polynomials up to Interdefinability  Abstract: Motivated by recent progress toward Zilber's Restricted Trichotomy Conjecture, we study reducts of the complex field up to interdefinability over parameters. Precisely, we will consider structures of the form (C, P_1,...,P_n), where C is set of complex numbers and the P_i are polynomial maps of potentially different arities. Somewhat surprisingly, our main result states that almost all such structures (in a precise sense) are interdefinable. The proof uses a mix of tools from geometric stability theory, combinatorics, and algebraic geometry. This is joint work with Chieu-Minh Tran. URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html

## Logic Seminar Wed 9 Nov 2022 17:00 hrs at NUS by Benjamin T Castle

NUS Logic Seminar
Invitation to the Logic Seminar at the National University of Singapore Date: Wednesday, 9 November 2022, 17:00 hrs Place: NUS, Department of Mathematics, S17#04-05 Speaker: Benjamin T Castle Title: Complex Polynomials up to Interdefinability  Abstract: Motivated by recent progress toward Zilber's Restricted Trichotomy Conjecture, we study reducts of the complex field up to interdefinability over parameters. Precisely, we will consider structures of the form (C, P_1,...,P_n), where C is set of complex numbers and the P_i are polynomial maps of potentially different arities. Somewhat surprisingly, our main result states that almost all such structures (in a precise sense) are interdefinable. The proof uses a mix of tools from geometric stability theory, combinatorics, and algebraic geometry. This is joint work with Chieu-Minh Tran. URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html

## Logic Seminar Wed 9 Nov 2022 17:00 hrs at NUS by Benjamin T Castle

NUS Logic Seminar
Invitation to the Logic Seminar at the National University of Singapore Date: Wednesday, 9 November 2022, 17:00 hrs Place: NUS, Department of Mathematics, S17#04-05 Speaker: Benjamin T Castle Title: Complex Polynomials up to Interdefinability  Abstract: Motivated by recent progress toward Zilber's Restricted Trichotomy Conjecture, we study reducts of the complex field up to interdefinability over parameters. Precisely, we will consider structures of the form (C, P_1,...,P_n), where C is set of complex numbers and the P_i are polynomial maps of potentially different arities. Somewhat surprisingly, our main result states that almost all such structures (in a precise sense) are interdefinable. The proof uses a mix of tools from geometric stability theory, combinatorics, and algebraic geometry. This is joint work with Chieu-Minh Tran. URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html

## UPDATE - This Week in Logic at CUNY

This Week in Logic at CUNY
Hi everyone,

The Models of Peano Arithmetic (MOPA) talk on November 8th will be given by Roman Kossak (CUNY), on Generalized quantifiers in arithmetic.  Apologies for this omission!

Best,
Jonas

This Week in Logic at CUNY:

- - - - Monday, Oct 31, 2022 - - - -

Rutgers Logic Seminar
Monday, October 31, 3:30pm, Rutgers University, Hill 705
Simon Thomas, Rutgers University
Invariant random subgroups and characters

Logic and Metaphysics Workshop
Date: Monday, Oct 31, 4.15-6.15 (NY time), GC 7315
Friederike Moltmann (CNRS, Côte d’Azur).
Title: The semantics of special quantification: Higher-order metaphysics and nominalization approaches

Abstract: Prior’s problem consists in the impossibility of replacing clausal complements of most attitude verbs by ‘ordinary’ NPs; only ‘special quantifiers’ that is, quantifiers like something permit a replacement, preserving grammaticality or the same reading of the verb;

(1) a. John claims that he won.
b. ??? John claims a proposition / some thing.
c. John claims something.

In my 2013 book Abstract Objects and the Semantics of Natural Language, I have shown how this generalizes to nonreferential complements of various other intensional predicates and argued for a Nominalization Theory of special quantifiers. In this talk, I will review and extend the range of linguistic generalizations that motivate the Nominalization Theory and show that they pose serious problems for a simple higher-order semantics of special quantifiers. I will outline a new version of the Nominalization Theory for special quantifiers with attitude verbs and address the question whether there can be a unified semantics of special quantifiers for the various contexts in which they display a nominalizing force.

- - - - Tuesday, Nov 1, 2022 - - - -

Models of Peano Arithmetic (MOPA)
Tuesday, November 1, 1:00pm
Virtual (email Victoria Gitman vgitman@nylogic.org for meeting id)

Ali Enayat, University of Gothenburg
Tightness, solidity, and internal categoricity: Part II

Inspired by a certain result about PA in Albert Visser's paper 'Categories of theories and interpretations', I introduced the notions of tightness and solidity (of an arbitrary theory) in my paper 'Variations on a Visserian theme'; using them Visser's result can be expressed as: PA is a solid theory (it is easy to show that solidity implies tightness). My aforementioned paper demonstrates that besides PA, certain other canonical theories such as Z_2 (Second Order Arithmetic), ZF, and KM (Kelley-Morse Class Theory) are also solid. The first talk in this series will present : (a) the proofs of solidity of PA and Z_2, and (b) the relationship between Väänänen's notion of internal categoricity with the notions of solidity and tightness. The second part will concentrate on establishing the failure of solidity/tightness of certain subtheories of PA and Z_2, including any subtheory of PA or Z_2 that is finitely axiomatizable.

- - - - Wednesday, Nov 2, 2022 - - - -

The New York City Category Theory Seminar
Department of Computer Science
Department of Mathematics
The Graduate Center of The City University of New York, Room 6417

Speaker:     Astra Kolomatskaia, Stony Brook.

Date and Time:     Wednesday November 2, 2022, 7:00 - 8:30 PM. IN PERSON TALK.

Title:     The Objective Metatheory of Simply Typed Lambda Calculus.

Abstract: Lambda calculus is the language of functions. One reduces the application of a function to an argument by substituting the argument for the function's formal parameter inside of the function's body. The result of such a reduction may have further instances of function application. We can write down expressions, such as ((λ f. f f) (λ f. f f)), in which this process does not terminate. In the presence of types, however, one has a normalisation theorem, which effectively states that "programs can be run". One proof of this theorem, which only works for the most elementary of type theories, is to assign some monotone well-founded invariant to a given reduction algorithm. A much more surprising proof proceeds by constructing the normal form of a term by structural recursion on the term's syntactic representation, without ever performing reduction. Such normalisation algorithms fall under the class of Normalisation by Evaluation. Since the accidental discovery of the first such algorithm, it was clear that NbE had some underlying categorical content, and, in 1995, Altenkirch, Hofmann, and Streicher published the first categorical normalisation proof. Discovering this content requires first asking the question “What is STLC?”, perhaps preceded by the question “What is a type theory?”. In this talk we will lay out the details of Altenkirch's seminal paper and explore conceptual refinements discovered in the process of its formalisation in Cubical Agda.

- - - - Thursday, Nov 3, 2022 - - - -

- - - - Friday, Nov 4, 2022 - - - -

Set Theory Seminar
CUNY Graduate Center, Friday, November 4, 12:15pm NY time, room 6495
Hybrid: Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Corey Switzer, University of Vienna
The Special Tree Number

A tree of height  with no cofinal branch is called special if it can be decomposed into countably many antichains or, equivalently if it carries a specializing function: a function  so that if  then  and  are incomparable in the tree ordering. It is known that there is always a non-special tree of size continuum, but the existence of a smaller one is independent of ZFC. Motivated by this we introduce the special tree number, , the least size of a tree of height  which is neither non-special nor has a cofinal branch. Classical facts imply that  can be smaller than essentially all well studied cardinal characteristics. Conversely in this talk we will show that  can be larger than , and both the left hand side and bottom row of the Cichon diagram. Thus  is independent of many well known cardinal invariants. Central to this result is an in depth investigation of the types of reals added by the Baumgartner specialization poset which we will discuss as well.

Logic Workshop
Hybrid (email Victoria Gitman for meeting id)
Friday November 4, 2:00pm-3:30pm, Room 6417

Dave Marker, University of Illinois at Chicago
Automorphisms of differentially closed fields

Answering a question of Russell Miller, we show that there are differentially closed fields with no non-trivial automorphisms.

Next Week in Logic at CUNY:

- - - - Monday, Nov 7, 2022 - - - -

Rutgers Logic Seminar
Monday, November 7, 3:30pm, Rutgers University, Hill 705
Simon Thomas, Rutgers University
Invariant random subgroups and characters
Nov 7th, Tom Benhamou, UIC

Logic and Metaphysics Workshop
Date: Monday, November 7, 4.15-6.15 (NY time), GC 7315

Victoria Gitman (CUNY).

Title: Set theory without the powerset axiom

Abstract: Many natural and useful set-theoretic structures fail to satisfy the Powerset axiom. For example, the universe of sets can be decomposed into the H_alpha-hierarchy, indexed by cardinals alpha, where each H_alpha consists of all sets whose transitive closure has size less than alpha. If alpha is a regular cardinal, then H_alpha satisfies all axioms of ZFC except, maybe, the Powerset axiom (it will only satisfy Powerset if alpha is inaccessible). Class forcing extensions of models of ZFC will often fail to satisfy ZFC, but if the class forcing is nice enough, then it will preserve all the axioms of ZFC except, maybe, the Powerset axiom. Finally, a strong second-order set theory, extending Kelley-Morse by adding a choice principle for classes (Choice Scheme), is bi-interpretable with a strong first-order set theory without the Powerset axiom. Thus working in a strong enough second-order set theory can be reinterpreted as working in a strong first-order set theory in which the Powerset axiom fails. It turns out that simply taking the axioms of ZFC and removing the Powerset axiom does not yield a robust set theory. I will discuss robust (and strong) axiomatizations of set theory without Powerset and how much of the standard set theoretic machinery is still effective even in the strongest theories in the absence of Powerset. Because of the bi-interpretability of a strong set theory without Powerset with Kelley-Morse plus Choice Scheme, these results will have consequences for which set theoretic machinery continues to work in set theories with classes. Time permitting, I will also talk about some unexpectedly strange models of set theory without Powerset.

- - - - Tuesday, Nov 8, 2022 - - - -

Models of Peano Arithmetic (MOPA)
Tuesday, November 8, 7:00pm
Virtual (email Victoria Gitman vgitman@nylogic.org for meeting id)
Roman Kossak, CUNY
Generalized quantifiers in arithmetic

This will be another talk in the MOPA series on the history of the subject.

The work on generalized quantifiers in formal systems of arithmetic was initiated in 1980 by Macintyre, motivated by the search for natural extensions of first-order arithmetic that are immune to the Kirby-Paris-Harrington style independence results. Some open questions posed by Macintyre were solved in a definitive way in 1982 by Schmerl and Simpson and after that Schmerl wrote two more papers on for Peano Arithmetic in the languages with Ramsay stationary quantifiers. Some results of Macintyre were obtained independently by Carl Morgenstern. All these papers, while very well written, are quite technical and not easily accessible for readers who are not familiar with more advanced tools of the model theory of arithmetic. I will survey the results suppressing most technical details. I will also talk about an attempt to use logic with stationary quantifiers to classify -like recursively saturated models of PA.

- - - - Wednesday, Nov 9, 2022 - - - -

The New York City Category Theory Seminar
Department of Computer Science
Department of Mathematics
The Graduate Center of The City University of New York, Room 6417

Speaker:     Andrei Rodin, University of Lorraine (Nancy, France).

Date and Time:     Wednesday November 9, 2022, 7:00 - 8:30 PM.

Title:     Kolmogorov's Calculus of Problems and Homotopy Type theory.

Abstract: A. N. Kolmogorov in 1932 proposed an original version of mathematical intuitionism where the concept of problem plays a central role, and which differs in its content from the versions of intuitionism developed by A. Heyting and other followers of L. Brouwer. The popular BHK-semantics of Intuitionistic logic follows Heyting's line and conceals the original features of Kolmogorov's logical ideas. Homotopy Type theory (HoTT) implies a formal distinction between sentences and higher-order constructions and thus provides a mathematical argument in favour of Kolmogorov's approach and against Heyting's approach. At the same time HoTT does not support the constructive notion of negation applicable to general problems, which is informally discussed by Kolmogorov in the same context. Formalisation of Kolmogorov-style constructive negation remains an interesting open problem.

- - - - Thursday, Nov 10, 2022 - - - -

- - - - Friday, Nov 11, 2022 - - - -

Set Theory Seminar
Friday, November 11, 12:15pm NY time
Virtual: Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Peter Holy, Technical University of Vienna

- - - - Other Logic News - - - -

- - - - Web Site - - - -

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

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

## Cross-Alps Logic Seminar (speaker: Jacopo Emmenegger)

Cross-Alps Logic Seminar
On Friday 04.11.2022 at 16:00
Jacopo Emmenegger (University of Genoa)
will give a talk on
Quotients and equality, (co)algebraically

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 2017 'Mathematical logic: models, sets, computability'.

## This Week in Logic at CUNY

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

- - - - Monday, Oct 31, 2022 - - - -

Rutgers Logic Seminar
Monday, October 31, 3:30pm, Rutgers University, Hill 705
Simon Thomas, Rutgers University
Invariant random subgroups and characters

Logic and Metaphysics Workshop
Date: Monday, Oct 31, 4.15-6.15 (NY time), GC 7315
Friederike Moltmann (CNRS, Côte d’Azur).
Title: The semantics of special quantification: Higher-order metaphysics and nominalization approaches

Abstract: Prior’s problem consists in the impossibility of replacing clausal complements of most attitude verbs by ‘ordinary’ NPs; only ‘special quantifiers’ that is, quantifiers like something permit a replacement, preserving grammaticality or the same reading of the verb;

(1) a. John claims that he won.
b. ??? John claims a proposition / some thing.
c. John claims something.

In my 2013 book Abstract Objects and the Semantics of Natural Language, I have shown how this generalizes to nonreferential complements of various other intensional predicates and argued for a Nominalization Theory of special quantifiers. In this talk, I will review and extend the range of linguistic generalizations that motivate the Nominalization Theory and show that they pose serious problems for a simple higher-order semantics of special quantifiers. I will outline a new version of the Nominalization Theory for special quantifiers with attitude verbs and address the question whether there can be a unified semantics of special quantifiers for the various contexts in which they display a nominalizing force.

- - - - Tuesday, Nov 1, 2022 - - - -

Models of Peano Arithmetic (MOPA)
Tuesday, November 1, 1:00pm
Virtual (email Victoria Gitman vgitman@nylogic.org for meeting id)

Ali Enayat, University of Gothenburg
Tightness, solidity, and internal categoricity: Part II

Inspired by a certain result about PA in Albert Visser's paper 'Categories of theories and interpretations', I introduced the notions of tightness and solidity (of an arbitrary theory) in my paper 'Variations on a Visserian theme'; using them Visser's result can be expressed as: PA is a solid theory (it is easy to show that solidity implies tightness). My aforementioned paper demonstrates that besides PA, certain other canonical theories such as Z_2 (Second Order Arithmetic), ZF, and KM (Kelley-Morse Class Theory) are also solid. The first talk in this series will present : (a) the proofs of solidity of PA and Z_2, and (b) the relationship between Väänänen's notion of internal categoricity with the notions of solidity and tightness. The second part will concentrate on establishing the failure of solidity/tightness of certain subtheories of PA and Z_2, including any subtheory of PA or Z_2 that is finitely axiomatizable.

- - - - Wednesday, Nov 2, 2022 - - - -

The New York City Category Theory Seminar
Department of Computer Science
Department of Mathematics
The Graduate Center of The City University of New York, Room 6417

Speaker:     Astra Kolomatskaia, Stony Brook.

Date and Time:     Wednesday November 2, 2022, 7:00 - 8:30 PM. IN PERSON TALK.

Title:     The Objective Metatheory of Simply Typed Lambda Calculus.

Abstract: Lambda calculus is the language of functions. One reduces the application of a function to an argument by substituting the argument for the function's formal parameter inside of the function's body. The result of such a reduction may have further instances of function application. We can write down expressions, such as ((λ f. f f) (λ f. f f)), in which this process does not terminate. In the presence of types, however, one has a normalisation theorem, which effectively states that "programs can be run". One proof of this theorem, which only works for the most elementary of type theories, is to assign some monotone well-founded invariant to a given reduction algorithm. A much more surprising proof proceeds by constructing the normal form of a term by structural recursion on the term's syntactic representation, without ever performing reduction. Such normalisation algorithms fall under the class of Normalisation by Evaluation. Since the accidental discovery of the first such algorithm, it was clear that NbE had some underlying categorical content, and, in 1995, Altenkirch, Hofmann, and Streicher published the first categorical normalisation proof. Discovering this content requires first asking the question “What is STLC?”, perhaps preceded by the question “What is a type theory?”. In this talk we will lay out the details of Altenkirch's seminal paper and explore conceptual refinements discovered in the process of its formalisation in Cubical Agda.

- - - - Thursday, Nov 3, 2022 - - - -

- - - - Friday, Nov 4, 2022 - - - -

Set Theory Seminar
CUNY Graduate Center, Friday, November 4, 12:15pm NY time, room 6495
Hybrid: Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Corey Switzer, University of Vienna
The Special Tree Number

A tree of height  with no cofinal branch is called special if it can be decomposed into countably many antichains or, equivalently if it carries a specializing function: a function  so that if  then  and  are incomparable in the tree ordering. It is known that there is always a non-special tree of size continuum, but the existence of a smaller one is independent of ZFC. Motivated by this we introduce the special tree number, , the least size of a tree of height  which is neither non-special nor has a cofinal branch. Classical facts imply that  can be smaller than essentially all well studied cardinal characteristics. Conversely in this talk we will show that  can be larger than , and both the left hand side and bottom row of the Cichon diagram. Thus  is independent of many well known cardinal invariants. Central to this result is an in depth investigation of the types of reals added by the Baumgartner specialization poset which we will discuss as well.

Logic Workshop
Hybrid (email Victoria Gitman for meeting id)
Friday November 4, 2:00pm-3:30pm, Room 6417

Dave Marker, University of Illinois at Chicago
Automorphisms of differentially closed fields

Answering a question of Russell Miller, we show that there are differentially closed fields with no non-trivial automorphisms.

Next Week in Logic at CUNY:

- - - - Monday, Nov 7, 2022 - - - -

Rutgers Logic Seminar
Monday, November 7, 3:30pm, Rutgers University, Hill 705
Simon Thomas, Rutgers University
Invariant random subgroups and characters
Nov 7th, Tom Benhamou, UIC

Logic and Metaphysics Workshop
Date: Monday, November 7, 4.15-6.15 (NY time), GC 7315

Victoria Gitman (CUNY).

Title: Set theory without the powerset axiom

Abstract: Many natural and useful set-theoretic structures fail to satisfy the Powerset axiom. For example, the universe of sets can be decomposed into the H_alpha-hierarchy, indexed by cardinals alpha, where each H_alpha consists of all sets whose transitive closure has size less than alpha. If alpha is a regular cardinal, then H_alpha satisfies all axioms of ZFC except, maybe, the Powerset axiom (it will only satisfy Powerset if alpha is inaccessible). Class forcing extensions of models of ZFC will often fail to satisfy ZFC, but if the class forcing is nice enough, then it will preserve all the axioms of ZFC except, maybe, the Powerset axiom. Finally, a strong second-order set theory, extending Kelley-Morse by adding a choice principle for classes (Choice Scheme), is bi-interpretable with a strong first-order set theory without the Powerset axiom. Thus working in a strong enough second-order set theory can be reinterpreted as working in a strong first-order set theory in which the Powerset axiom fails. It turns out that simply taking the axioms of ZFC and removing the Powerset axiom does not yield a robust set theory. I will discuss robust (and strong) axiomatizations of set theory without Powerset and how much of the standard set theoretic machinery is still effective even in the strongest theories in the absence of Powerset. Because of the bi-interpretability of a strong set theory without Powerset with Kelley-Morse plus Choice Scheme, these results will have consequences for which set theoretic machinery continues to work in set theories with classes. Time permitting, I will also talk about some unexpectedly strange models of set theory without Powerset.

- - - - Tuesday, Nov 8, 2022 - - - -

Models of Peano Arithmetic (MOPA)
Tuesday, November 8, 7:00pm
Virtual (email Victoria Gitman vgitman@nylogic.org for meeting id)

This will be another talk in the MOPA series on the history of the subject.

The work on generalized quantifiers in formal systems of arithmetic was initiated in 1980 by Macintyre, motivated by the search for natural extensions of first-order arithmetic that are immune to the Kirby-Paris-Harrington style independence results. Some open questions posed by Macintyre were solved in a definitive way in 1982 by Schmerl and Simpson and after that Schmerl wrote two more papers on for Peano Arithmetic in the languages with Ramsay stationary quantifiers. Some results of Macintyre were obtained independently by Carl Morgenstern. All these papers, while very well written, are quite technical and not easily accessible for readers who are not familiar with more advanced tools of the model theory of arithmetic. I will survey the results suppressing most technical details. I will also talk about an attempt to use logic with stationary quantifiers to classify -like recursively saturated models of PA.

- - - - Wednesday, Nov 9, 2022 - - - -

The New York City Category Theory Seminar
Department of Computer Science
Department of Mathematics
The Graduate Center of The City University of New York, Room 6417

Speaker:     Andrei Rodin, University of Lorraine (Nancy, France).

Date and Time:     Wednesday November 9, 2022, 7:00 - 8:30 PM.

Title:     Kolmogorov's Calculus of Problems and Homotopy Type theory.

Abstract: A. N. Kolmogorov in 1932 proposed an original version of mathematical intuitionism where the concept of problem plays a central role, and which differs in its content from the versions of intuitionism developed by A. Heyting and other followers of L. Brouwer. The popular BHK-semantics of Intuitionistic logic follows Heyting's line and conceals the original features of Kolmogorov's logical ideas. Homotopy Type theory (HoTT) implies a formal distinction between sentences and higher-order constructions and thus provides a mathematical argument in favour of Kolmogorov's approach and against Heyting's approach. At the same time HoTT does not support the constructive notion of negation applicable to general problems, which is informally discussed by Kolmogorov in the same context. Formalisation of Kolmogorov-style constructive negation remains an interesting open problem.

- - - - Thursday, Nov 10, 2022 - - - -

- - - - Friday, Nov 11, 2022 - - - -

Set Theory Seminar
Friday, November 11, 12:15pm NY time
Virtual: Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Peter Holy, Technical University of Vienna

- - - - Other Logic News - - - -

- - - - Web Site - - - -

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

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

## Barcelona Set Theory Seminar

Barcelona Logic Seminar

Dear All,
Please find attached the announcement of the next Barcelona Set Theory Seminar session.

SPEAKER:   Philipp Lücke
TITLE: Rowbottom cardinals and definability
DATE: Wednesday, 2 November 2022
TIME: 16:00 (CEST)
PLACE: Room B1 (UB). The Seminar can also be followed online via Zoom:

Best regards,
Joan

P.S.: If you do not wish to receive any more announcements, please send an email to bagaria@ub.edu with the text “Unsubscribe”.

Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia

Phone: +34 93 402 1609
joan.bagaria@icrea.cat
bagaria@ub.edu

## Core Model Seminar on Tuesday

Carnegie Mellon Logic Seminar
TUESDAY, November 1, 2022 Core Model Seminar: 1:30 - 3 PM Eastern, Online, Derek Levinson, University of California, Los Angeles Join Zoom Meeting: https://cmu.zoom.us/j/97749733438?pwd=Yk5PcSsvekptWWxMNUhCU2pFbzA0Zz09 Meeting ID: 977 4973 3438 Passcode: 457791 TITLE: Unreachability of Pointclasses in $L(R)$, part 2 ABSTRACT: We present Hjorth's proof that there is no sequence of distinct $\Sigma^1_2$ sets of length $\delta^1_2$. Then we prove in $L(R)$ if $\Gamma$ is an inductive-like pointclass then there is no sequence of distinct $\Gamma$ sets of length $\delta_\Gamma^+$. ORGANIZERS' NOTE: If you'd like access to our archives of presentation materials and recordings, please ask Ernest Schimmerling.

## (KGRC) two(!) seminar talks on Thursday, November 3

Kurt Godel Research Center
The KGRC welcomes as guests: Martin Hils (host: Matthias Aschenbrenner) visits the KGRC until March 31, 2023 and gives a talk on January 19, 2023 (details to be announced at a later time). Franz-Viktor Kuhlmann (host: Matthias Aschenbrenner) visits the KGRC from November 1 until January 31, 2023 and gives a talk on November 24 (details to be announced at a later time). Will Brian (host: Vera Fischer) visits the KGRC from November 1 to November 6 and gives two talks (see below). Simone Ramello (host: Martin Hils) visits the KGRC from November 3 to November 8. David Chodounsky (host: Vera Fischer) visits the KGRC from December 4 until December 8 and gives a talk on December 6 (details to be announced at a later time). Jan Hubicka (host: Vera Fischer) visits the KGRC from December 5 until December 8 and gives a talk on December 6 (details to be announced at a later time). Stefan Ludwig (hosts: Martin Hils and Matthias Aschenbrenner) visits the KGRC from December 5 to December 14. * * * Logic Colloquium Kurt Gödel Research Center Thursday, November 3 "Covering versus partitioning with Polish spaces" Will Brian (UNC Charlotte, US) A topological space is Polish if it is second countable and completely metrizable. We may think of these as the small, or "essentially countable" members of the category of completely metrizable spaces. In this talk, we explore the question of whether, given a completely metrizable space $X$, it is possible to cover $X$ with fewer Polish spaces than it can be partitioned into. Surprisingly, this question not only turns out to be independent of ZFC, but proving its independence requires large cardinal axioms. I will sketch some of the ideas that go into one direction of this independence proof. Specifically, I will describe how a version of the model-theoretic transfer principle called Chang's Conjecture implies that there is a completely metrizable space that can be covered with fewer Polish spaces than it can be partitioned into. Time and Place Talk at 3:00pm in hybrid mode, in person as well as via Zoom. (Students at Uni Wien are required to attend in person.) Universität Wien Institut für Mathematik Kolingasse 14-16 1090 Wien 1st floor Seminar room 10 For details about how to join the Zoom session, please see the end of this message. * * * Set Theory Research Seminar Kurt Gödel Research Center Thursday, November 3 (Please note the unusual day, time and place!) "Partitioning the real line into Borel sets" Will Brian (UNC Charlotte, US) I will sketch a proof that, assuming $0^\dagger$ does not exist, if there is a partition of the real line $\mathbb{R}$ into $\aleph_\omega$ Borel sets, then there is also a partition of $\mathbb{R}$ into $\aleph_{\omega+1}$ Borel sets. (And the same is true for any singular cardinal of countable cofinality in place of $\aleph_\omega$.) This contrasts starkly with the situation for successor-of-successor cardinals, where the spectrum of possible sizes of partitions of $\mathbb{R}$ into Borel sets can seemingly be made completely arbitrary. For example, given any $A \subseteq \omega$ with $0, 1 \in A$, there is a forcing extension in which $A = \{n < \omega :$ there is a partition of $\mathbb{R}$ into $\aleph_n$ Borel sets$\}$. Time and Place Talk at 4:45pm in hybrid mode, in person as well as via Zoom. (Students at Uni Wien are required to attend in person.) Universität Wien Institut für Mathematik Oskar-Morgenstern-Platz 1 1090 Wien 2nd floor Seminar room 14 Zoom: If you need the Zoom data and have not received the meeting link by the day before the talk, please contact richard.springer@univie.ac.at! (Please direct any other requests about the seminars and Zoom meeting(s) to vera.fischer@univie.ac.at.)

## Wednesday seminar

Prague Set Theory Seminar
Dear all, The seminar meets on Wednesday November 2nd at 11:00 in the Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building. Please note that the open days of the Institute will take place next week, so expect children running around and other minor inconveniences. Program: Chris Lambie Hanson -- Partition relations on Polish spaces We study partition relations on Polish spaces, asserting that arbitrary colorings of products of uncountable Polish spaces have "large" monochromatic subsets (for example, products of somewhere dense subsets on which the coloring is constant). We will discuss situations in which such partition relations provably do or do not hold and will prove a sharp result indicating the effect of such relations on the value of the continuum. Time and interest permitting, we will also discuss connections with the Halpern-Lauchli theorem and its variations. This is joint work with Andy Zucker. Best, David

## Logic Seminar Wed 2 Nov 2022 17:00 hrs at NUS by Wu Guohua

NUS Logic Seminar
Invitation to the Logic Seminar at the National University of Singapore Date: Wednesday, 02 November 2022, 17:00 hrs Place: NUS, Department of Mathematics, S17#04-05 Speaker: Wu Guohua Title: Ring constructions: axioms needed Abstract: Many constructions in rings involve applications of various axioms, which guarantee the existence of wanted objects. In this talk, I will present examples of such constructions, and show how these axioms are applied and really needed. URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html

## Logic Seminar 26 October 2022 17:00 hrs at NUS by Sun Mengzhou

NUS Logic Seminar
Invitation to the Logic Seminar at the National University of Singapore Date: Wednesday, 26 October 2022, 17:00 hrs Place: NUS, Department of Mathematics, S17#04-05 Speaker: Sun Mengzhou Title: End extensions of weak arithmetic theories Abstract: Paris and Kirby showed that a countable model satisfies B Sigma_{n+2} if and only if it has an (n+2)-elementary proper end extension. Later Kaufman asked whether we can always extend countable models of B Sigma_{n+2} to some model of B Sigma_{n+1}. We briefly discuss what we have now related to this question and what is the difficulty here. URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html

## UPDATE - This Week in Logic at CUNY

This Week in Logic at CUNY
Hi everyone,

Just an update - David Marker's talk in the Logic Workshop will take place on Friday, November 4th (it was erroneously marked as this Friday, October 28).

Apologies for this error,
Jonas

This Week in Logic at CUNY:

- - - - Monday, Oct 24, 2022 - - - -

Rutgers Logic Seminar
Monday, October 24, 3:30pm, Rutgers University, Hill 705
Corey Switzer, University of Vienna
The Special Tree Number

Logic and Metaphysics Workshop
Date: Monday, Oct 24, 4.15-6.15 (NY time), GC 7315
Tomorrow, Monday, October 24th, 4.15-6.15 (NY time)
Speaker: Rohit Parikh (CUNY)
Speaker Medium: In-person at the Graduate Center, Room 7314 (you may also attend virtually).
Title: A measure of group coherence

Abstract: The Stanford Encyclopedia of Philosophy has an article on Social Epistemology and also one on group rights. Wikipedia has an article on group coherence. Clearly, groups are important and that importance is acknowledged. But what is missing is a measure of group coherence or as I shall say, groupiness. The Democratic party is a group but the Squad is a more coherent subgroup and works more closely with each other. The bees in a beehive work coherently with each other but it is not clear if this coherence is buttressed by common beliefs. The purpose of this talk, and of this project is to propose a measure of groupiness, investigate its properties, ask about the extent to which it enables group action, and about the extent to which it comports with epistemic logic and with the theory of information.

- - - - Tuesday, Oct 25, 2022 - - - -

Models of Peano Arithmetic (MOPA)
Tuesday, October 25, 1:00pm
Virtual (email Victoria Gitman vgitman@nylogic.org for meeting id)

Ali Enayat, University of Gothenburg
Tightness, solidity, and internal categoricity

Inspired by a certain result about PA in Albert Visser's paper 'Categories of theories and interpretations', I introduced the notions of tightness and solidity (of an arbitrary theory) in my paper 'Variations on a Visserian theme'; using them Visser's result can be expressed as: PA is a solid theory (it is easy to show that solidity implies tightness). My aforementioned paper demonstrates that besides PA, certain other canonical theories such as Z_2 (Second Order Arithmetic), ZF, and KM (Kelley-Morse Class Theory) are also solid. The first talk in this series will present : (a) the proofs of solidity of PA and Z_2, and (b) the relationship between Väänänen's notion of internal categoricity with the notions of solidity and tightness. The second part will concentrate on establishing the failure of solidity/tightness of certain subtheories of PA and Z_2, including any subtheory of PA or Z_2 that is finitely axiomatizable.

Computational Logic Seminar
Tuesday, October 25, Time 2:00 - 4:00 PM, Room 3310-B,
For a zoom link contact SArtemov@gmail.com
Speaker: Sergei Artemov, Graduate Center CUNY
Title: How to Prove, and Not to Prove, Consistency

Abstract:
The consistency of a formal theory is a sequential property C = {C_0, C_1, ... C_n, ...}, where each C_n states that the n-th derivation does not contain a contradiction. For proving C in a theory T, Hilbert suggested (i) finding a procedure that given n builds a T-proof of C_n and (ii) proving in T that this procedure always works.

However, for Peano Arithmetic PA, the traditional way here has been to compress C into a single arithmetical formula Consis(PA) and apply the Second Gödel Incompleteness theorem, stating the unprovability of Consis(PA) in PA, to claim the unprovability of C in PA. This chain of reasoning is fundamentally flawed: one can only conclude that (a compressed form of) consistency is not provable in a FINITE fragment of PA whereas PA is known to be (much) stronger than any of its finite fragments.

Following the original Hilbert's approach, we were able to show that the consistency property of PA is indeed provable in PA. These findings dismantle a foundational “impossibility paradigm”: there exists no consistency proof of a system that can be formalized in the system itself. (Encyclopaedia Britannica, Article "Metalogic," 2000).

- - - - Wednesday, Oct 26, 2022 - - - -

The New York City Category Theory Seminar
Department of Computer Science
Department of Mathematics
The Graduate Center of The City University of New York, Room 6417

Speaker:     Ross Street, Macquarie University.

Date and Time:     Wednesday October 26, 2022, 7:00 - 8:30 PM.

Title:     The core groupoid can suffice.

Abstract: Let V be the monoidal category of modules over a commutative ring R. I am interested in categories A for which there is a groupoid G such that the functor categories [A,V] and [G,V] are equivalent. In particular, G could be the core groupoid of A; that is, the subcategory with the same objects and with only the invertible morphisms. Every category A can be regarded as a V-category (that is, an R-linear category), denoted RA, with the same objects and with hom R-module RA(a,b) free on the homset A(a,b). Indeed, RA is the free V-category on A so that the V-functor category [RA,V] is the ordinary functor category [A,V] with the pointwise R-linear structure. In these terms, we are interested in when RA and RG are Morita equivalent V-categories. In my joint work with Steve Lack on Dold-Kan-type equivalences, we had many examples of this phenomenon. However, the example of Nick Kuhn, where A is the category of finite vector spaces over a fixed finite field F with all F-linear functions and G is the general linear groupoid over F, does not fit our theory. Yet the kernel'' of the equivalence is of the same type. The present work shows that the category theory behind the Kuhn result also covers our Dold-Kan-type setting. I plan to start with a baby example which highlights the ideas.

I am grateful to Nick Kuhn and Ben Steinberg for their patient email correspondence with me on this topic.

- - - - Thursday, Oct 27, 2022 - - - -

- - - - Friday, Oct 28, 2022 - - - -

Set Theory Seminar
CUNY Graduate Center, Friday, October 28, 12:15pm NY time
Virtual: Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Andreas Lietz, University of Münster

Forcing ' is -dense' from Large Cardinals - A Journey guided by the Stars: Part II

An ideal  on  is -dense if  has a dense subset of size . We prove, assuming large cardinals, that there is a semiproper forcing  so thatThis answers a question of Woodin positively. Our general strategy is based on the observation that replacing the role of  in Woodin's axiom  by  results in an axiom  which implies .
We proceed in three steps: First we define and motivate a new forcing axiom  and then modify the Asperó-Schindler proof of  to show . Finally, assuming a supercompact limit of supercompact cardinals exists, we construct a semiproper partial order forcing . This last step involves proving two new iteration theorems both of which allow for forcings killing stationary sets.

Logic Workshop
Hybrid (email Victoria Gitman for meeting id)
Friday October 28, 2:00pm-3:30pm, Room 6417
Corey Switzer University of Vienna

Ideal Independence, Filters and Maximal Sets of Reals

A family  is called ideal independent if given any finite, distinct , the set  is infinite. In other words, the ideal generated by  does not contain  for any . The least size of a maximal (with respect to inclusion) ideal independent family is denoted  and has recently been tied to several interesting questions in cardinal characteristics and Boolean algebra theory. In this talk we will sketch our new proof that this number is ZFC-provably greater than or equal to the ultrafilter number – the least size of a base for a non-principal ultrafilter on . The proof is entirely combinatorial and relies only on a knowledge of ultrafilters and their properties. Time permitting, we will also discuss some interesting new applications of ideal independent families to topology via a generalization of Mrowka spaces usually studied for almost disjoint families. This is joint work with Serhii Bardyla, Jonathan Cancino and Vera Fischer.

Next Week in Logic at CUNY:

- - - - Monday, Oct 31, 2022 - - - -

Rutgers Logic Seminar
Monday, October 31, 3:30pm, Rutgers University, Hill 705
Simon Thomas, Rutgers University
Invariant random subgroups and characters

Logic and Metaphysics Workshop
Date: Monday, Oct 31, 4.15-6.15 (NY time), GC 7315
Friederike Moltmann (CNRS, Côte d’Azur).
Title: The semantics of special quantification: Higher-order metaphysics and nominalization approaches

Abstract: Prior’s problem consists in the impossibility of replacing clausal complements of most attitude verbs by ‘ordinary’ NPs; only ‘special quantifiers’ that is, quantifiers like something permit a replacement, preserving grammaticality or the same reading of the verb;

(1) a. John claims that he won.
b. ??? John claims a proposition / some thing.
c. John claims something.

In my 2013 book Abstract Objects and the Semantics of Natural Language, I have shown how this generalizes to nonreferential complements of various other intensional predicates and argued for a Nominalization Theory of special quantifiers. In this talk, I will review and extend the range of linguistic generalizations that motivate the Nominalization Theory and show that they pose serious problems for a simple higher-order semantics of special quantifiers. I will outline a new version of the Nominalization Theory for special quantifiers with attitude verbs and address the question whether there can be a unified semantics of special quantifiers for the various contexts in which they display a nominalizing force.

- - - - Tuesday, Nov 1, 2022 - - - -

Models of Peano Arithmetic (MOPA)
Tuesday, November 1, 1:00pm
Virtual (email Victoria Gitman vgitman@nylogic.org for meeting id)

Ali Enayat, University of Gothenburg
Tightness, solidity, and internal categoricity: Part II

Inspired by a certain result about PA in Albert Visser's paper 'Categories of theories and interpretations', I introduced the notions of tightness and solidity (of an arbitrary theory) in my paper 'Variations on a Visserian theme'; using them Visser's result can be expressed as: PA is a solid theory (it is easy to show that solidity implies tightness). My aforementioned paper demonstrates that besides PA, certain other canonical theories such as Z_2 (Second Order Arithmetic), ZF, and KM (Kelley-Morse Class Theory) are also solid. The first talk in this series will present : (a) the proofs of solidity of PA and Z_2, and (b) the relationship between Väänänen's notion of internal categoricity with the notions of solidity and tightness. The second part will concentrate on establishing the failure of solidity/tightness of certain subtheories of PA and Z_2, including any subtheory of PA or Z_2 that is finitely axiomatizable.

- - - - Wednesday, Nov 2, 2022 - - - -

The New York City Category Theory Seminar
Department of Computer Science
Department of Mathematics
The Graduate Center of The City University of New York, Room 6417

Speaker:     Astra Kolomatskaia, Stony Brook.

Date and Time:     Wednesday November 2, 2022, 7:00 - 8:30 PM. IN PERSON TALK.

Title:     The Objective Metatheory of Simply Typed Lambda Calculus.

Abstract: Lambda calculus is the language of functions. One reduces the application of a function to an argument by substituting the argument for the function's formal parameter inside of the function's body. The result of such a reduction may have further instances of function application. We can write down expressions, such as ((λ f. f f) (λ f. f f)), in which this process does not terminate. In the presence of types, however, one has a normalisation theorem, which effectively states that "programs can be run". One proof of this theorem, which only works for the most elementary of type theories, is to assign some monotone well-founded invariant to a given reduction algorithm. A much more surprising proof proceeds by constructing the normal form of a term by structural recursion on the term's syntactic representation, without ever performing reduction. Such normalisation algorithms fall under the class of Normalisation by Evaluation. Since the accidental discovery of the first such algorithm, it was clear that NbE had some underlying categorical content, and, in 1995, Altenkirch, Hofmann, and Streicher published the first categorical normalisation proof. Discovering this content requires first asking the question “What is STLC?”, perhaps preceded by the question “What is a type theory?”. In this talk we will lay out the details of Altenkirch's seminal paper and explore conceptual refinements discovered in the process of its formalisation in Cubical Agda.

- - - - Thursday, Nov 3, 2022 - - - -

- - - - Friday, Nov 4, 2022 - - - -

Set Theory Seminar
CUNY Graduate Center, Friday, November 4, 12:15pm NY time, room 6495
Hybrid: Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Corey Switzer, University of Vienna
The Special Tree Number

A tree of height  with no cofinal branch is called special if it can be decomposed into countably many antichains or, equivalently if it carries a specializing function: a function  so that if  then  and  are incomparable in the tree ordering. It is known that there is always a non-special tree of size continuum, but the existence of a smaller one is independent of ZFC. Motivated by this we introduce the special tree number, , the least size of a tree of height  which is neither non-special nor has a cofinal branch. Classical facts imply that  can be smaller than essentially all well studied cardinal characteristics. Conversely in this talk we will show that  can be larger than , and both the left hand side and bottom row of the Cichon diagram. Thus  is independent of many well known cardinal invariants. Central to this result is an in depth investigation of the types of reals added by the Baumgartner specialization poset which we will discuss as well.

Logic Workshop
Hybrid (email Victoria Gitman for meeting id)
Friday November 4, 2:00pm-3:30pm, Room 6417

Dave Marker, University of Illinois at Chicago
Automorphisms of differentially closed fields

Answering a question of Russell Miller, we show that there are differentially closed fields with no non-trivial automorphisms.

- - - - Other Logic News - - - -

- - - - Web Site - - - -

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

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

## This Week in Logic at CUNY

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

- - - - Monday, Oct 24, 2022 - - - -

Rutgers Logic Seminar
Monday, October 24, 3:30pm, Rutgers University, Hill 705
Corey Switzer, University of Vienna
The Special Tree Number

Logic and Metaphysics Workshop
Date: Monday, Oct 24, 4.15-6.15 (NY time), GC 7315
Tomorrow, Monday, October 24th, 4.15-6.15 (NY time)
Speaker: Rohit Parikh (CUNY)
Speaker Medium: In-person at the Graduate Center, Room 7314 (you may also attend virtually).
Title: A measure of group coherence

Abstract: The Stanford Encyclopedia of Philosophy has an article on Social Epistemology and also one on group rights. Wikipedia has an article on group coherence. Clearly, groups are important and that importance is acknowledged. But what is missing is a measure of group coherence or as I shall say, groupiness. The Democratic party is a group but the Squad is a more coherent subgroup and works more closely with each other. The bees in a beehive work coherently with each other but it is not clear if this coherence is buttressed by common beliefs. The purpose of this talk, and of this project is to propose a measure of groupiness, investigate its properties, ask about the extent to which it enables group action, and about the extent to which it comports with epistemic logic and with the theory of information.

- - - - Tuesday, Oct 25, 2022 - - - -

Models of Peano Arithmetic (MOPA)
Tuesday, October 25, 1:00pm
Virtual (email Victoria Gitman vgitman@nylogic.org for meeting id)

Ali Enayat, University of Gothenburg
Tightness, solidity, and internal categoricity

Inspired by a certain result about PA in Albert Visser's paper 'Categories of theories and interpretations', I introduced the notions of tightness and solidity (of an arbitrary theory) in my paper 'Variations on a Visserian theme'; using them Visser's result can be expressed as: PA is a solid theory (it is easy to show that solidity implies tightness). My aforementioned paper demonstrates that besides PA, certain other canonical theories such as Z_2 (Second Order Arithmetic), ZF, and KM (Kelley-Morse Class Theory) are also solid. The first talk in this series will present : (a) the proofs of solidity of PA and Z_2, and (b) the relationship between Väänänen's notion of internal categoricity with the notions of solidity and tightness. The second part will concentrate on establishing the failure of solidity/tightness of certain subtheories of PA and Z_2, including any subtheory of PA or Z_2 that is finitely axiomatizable.

Computational Logic Seminar
Tuesday, October 25, Time 2:00 - 4:00 PM, Room 3310-B,
For a zoom link contact SArtemov@gmail.com
Speaker: Sergei Artemov, Graduate Center CUNY
Title: How to Prove, and Not to Prove, Consistency

Abstract:
The consistency of a formal theory is a sequential property C = {C_0, C_1, ... C_n, ...}, where each C_n states that the n-th derivation does not contain a contradiction. For proving C in a theory T, Hilbert suggested (i) finding a procedure that given n builds a T-proof of C_n and (ii) proving in T that this procedure always works.

However, for Peano Arithmetic PA, the traditional way here has been to compress C into a single arithmetical formula Consis(PA) and apply the Second Gödel Incompleteness theorem, stating the unprovability of Consis(PA) in PA, to claim the unprovability of C in PA. This chain of reasoning is fundamentally flawed: one can only conclude that (a compressed form of) consistency is not provable in a FINITE fragment of PA whereas PA is known to be (much) stronger than any of its finite fragments.

Following the original Hilbert's approach, we were able to show that the consistency property of PA is indeed provable in PA. These findings dismantle a foundational “impossibility paradigm”: there exists no consistency proof of a system that can be formalized in the system itself. (Encyclopaedia Britannica, Article "Metalogic," 2000).

- - - - Wednesday, Oct 26, 2022 - - - -

The New York City Category Theory Seminar
Department of Computer Science
Department of Mathematics
The Graduate Center of The City University of New York, Room 6417

Speaker:     Ross Street, Macquarie University.

Date and Time:     Wednesday October 26, 2022, 7:00 - 8:30 PM.

Title:     The core groupoid can suffice.

Abstract: Let V be the monoidal category of modules over a commutative ring R. I am interested in categories A for which there is a groupoid G such that the functor categories [A,V] and [G,V] are equivalent. In particular, G could be the core groupoid of A; that is, the subcategory with the same objects and with only the invertible morphisms. Every category A can be regarded as a V-category (that is, an R-linear category), denoted RA, with the same objects and with hom R-module RA(a,b) free on the homset A(a,b). Indeed, RA is the free V-category on A so that the V-functor category [RA,V] is the ordinary functor category [A,V] with the pointwise R-linear structure. In these terms, we are interested in when RA and RG are Morita equivalent V-categories. In my joint work with Steve Lack on Dold-Kan-type equivalences, we had many examples of this phenomenon. However, the example of Nick Kuhn, where A is the category of finite vector spaces over a fixed finite field F with all F-linear functions and G is the general linear groupoid over F, does not fit our theory. Yet the kernel'' of the equivalence is of the same type. The present work shows that the category theory behind the Kuhn result also covers our Dold-Kan-type setting. I plan to start with a baby example which highlights the ideas.

I am grateful to Nick Kuhn and Ben Steinberg for their patient email correspondence with me on this topic.

- - - - Thursday, Oct 27, 2022 - - - -

- - - - Friday, Oct 28, 2022 - - - -

Set Theory Seminar
CUNY Graduate Center, Friday, October 28, 12:15pm NY time
Virtual: Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Andreas Lietz, University of Münster

Forcing ' is -dense' from Large Cardinals - A Journey guided by the Stars: Part II

An ideal  on  is -dense if  has a dense subset of size . We prove, assuming large cardinals, that there is a semiproper forcing  so thatThis answers a question of Woodin positively. Our general strategy is based on the observation that replacing the role of  in Woodin's axiom  by  results in an axiom  which implies .
We proceed in three steps: First we define and motivate a new forcing axiom  and then modify the Asperó-Schindler proof of  to show . Finally, assuming a supercompact limit of supercompact cardinals exists, we construct a semiproper partial order forcing . This last step involves proving two new iteration theorems both of which allow for forcings killing stationary sets.

Logic Workshop
Hybrid (email Victoria Gitman for meeting id)
Friday October 28, 2:00pm-3:30pm, Room 6417
Corey Switzer University of Vienna

Ideal Independence, Filters and Maximal Sets of Reals

A family  is called ideal independent if given any finite, distinct , the set  is infinite. In other words, the ideal generated by  does not contain  for any . The least size of a maximal (with respect to inclusion) ideal independent family is denoted  and has recently been tied to several interesting questions in cardinal characteristics and Boolean algebra theory. In this talk we will sketch our new proof that this number is ZFC-provably greater than or equal to the ultrafilter number – the least size of a base for a non-principal ultrafilter on . The proof is entirely combinatorial and relies only on a knowledge of ultrafilters and their properties. Time permitting, we will also discuss some interesting new applications of ideal independent families to topology via a generalization of Mrowka spaces usually studied for almost disjoint families. This is joint work with Serhii Bardyla, Jonathan Cancino and Vera Fischer.

Next Week in Logic at CUNY:

- - - - Monday, Oct 31, 2022 - - - -

Rutgers Logic Seminar
Monday, October 31, 3:30pm, Rutgers University, Hill 705
Simon Thomas, Rutgers University
Invariant random subgroups and characters

Logic and Metaphysics Workshop
Date: Monday, Oct 31, 4.15-6.15 (NY time), GC 7315
Friederike Moltmann (CNRS, Côte d’Azur).
Title: The semantics of special quantification: Higher-order metaphysics and nominalization approaches

Abstract: Prior’s problem consists in the impossibility of replacing clausal complements of most attitude verbs by ‘ordinary’ NPs; only ‘special quantifiers’ that is, quantifiers like something permit a replacement, preserving grammaticality or the same reading of the verb;

(1) a. John claims that he won.
b. ??? John claims a proposition / some thing.
c. John claims something.

In my 2013 book Abstract Objects and the Semantics of Natural Language, I have shown how this generalizes to nonreferential complements of various other intensional predicates and argued for a Nominalization Theory of special quantifiers. In this talk, I will review and extend the range of linguistic generalizations that motivate the Nominalization Theory and show that they pose serious problems for a simple higher-order semantics of special quantifiers. I will outline a new version of the Nominalization Theory for special quantifiers with attitude verbs and address the question whether there can be a unified semantics of special quantifiers for the various contexts in which they display a nominalizing force.

- - - - Tuesday, Nov 1, 2022 - - - -

Models of Peano Arithmetic (MOPA)
Tuesday, November 1, 1:00pm
Virtual (email Victoria Gitman vgitman@nylogic.org for meeting id)

Ali Enayat, University of Gothenburg
Tightness, solidity, and internal categoricity: Part II

Inspired by a certain result about PA in Albert Visser's paper 'Categories of theories and interpretations', I introduced the notions of tightness and solidity (of an arbitrary theory) in my paper 'Variations on a Visserian theme'; using them Visser's result can be expressed as: PA is a solid theory (it is easy to show that solidity implies tightness). My aforementioned paper demonstrates that besides PA, certain other canonical theories such as Z_2 (Second Order Arithmetic), ZF, and KM (Kelley-Morse Class Theory) are also solid. The first talk in this series will present : (a) the proofs of solidity of PA and Z_2, and (b) the relationship between Väänänen's notion of internal categoricity with the notions of solidity and tightness. The second part will concentrate on establishing the failure of solidity/tightness of certain subtheories of PA and Z_2, including any subtheory of PA or Z_2 that is finitely axiomatizable.

- - - - Wednesday, Nov 2, 2022 - - - -

The New York City Category Theory Seminar
Department of Computer Science
Department of Mathematics
The Graduate Center of The City University of New York, Room 6417

Speaker:     Astra Kolomatskaia, Stony Brook.

Date and Time:     Wednesday November 2, 2022, 7:00 - 8:30 PM. IN PERSON TALK.

Title:     The Objective Metatheory of Simply Typed Lambda Calculus.

Abstract: Lambda calculus is the language of functions. One reduces the application of a function to an argument by substituting the argument for the function's formal parameter inside of the function's body. The result of such a reduction may have further instances of function application. We can write down expressions, such as ((λ f. f f) (λ f. f f)), in which this process does not terminate. In the presence of types, however, one has a normalisation theorem, which effectively states that "programs can be run". One proof of this theorem, which only works for the most elementary of type theories, is to assign some monotone well-founded invariant to a given reduction algorithm. A much more surprising proof proceeds by constructing the normal form of a term by structural recursion on the term's syntactic representation, without ever performing reduction. Such normalisation algorithms fall under the class of Normalisation by Evaluation. Since the accidental discovery of the first such algorithm, it was clear that NbE had some underlying categorical content, and, in 1995, Altenkirch, Hofmann, and Streicher published the first categorical normalisation proof. Discovering this content requires first asking the question “What is STLC?”, perhaps preceded by the question “What is a type theory?”. In this talk we will lay out the details of Altenkirch's seminal paper and explore conceptual refinements discovered in the process of its formalisation in Cubical Agda.

- - - - Thursday, Nov 3, 2022 - - - -

- - - - Friday, Nov 4, 2022 - - - -

Set Theory Seminar
CUNY Graduate Center, Friday, November 4, 12:15pm NY time, room 6495
Hybrid: Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Corey Switzer, University of Vienna
The Special Tree Number

A tree of height  with no cofinal branch is called special if it can be decomposed into countably many antichains or, equivalently if it carries a specializing function: a function  so that if  then  and  are incomparable in the tree ordering. It is known that there is always a non-special tree of size continuum, but the existence of a smaller one is independent of ZFC. Motivated by this we introduce the special tree number, , the least size of a tree of height  which is neither non-special nor has a cofinal branch. Classical facts imply that  can be smaller than essentially all well studied cardinal characteristics. Conversely in this talk we will show that  can be larger than , and both the left hand side and bottom row of the Cichon diagram. Thus  is independent of many well known cardinal invariants. Central to this result is an in depth investigation of the types of reals added by the Baumgartner specialization poset which we will discuss as well.

Logic Workshop
Hybrid (email Victoria Gitman for meeting id)
Friday October 28, 2:00pm-3:30pm, Room 6417

Dave Marker, University of Illinois at Chicago
Automorphisms of differentially closed fields

Answering a question of Russell Miller, we show that there are differentially closed fields with no non-trivial automorphisms.

- - - - Other Logic News - - - -

- - - - Web Site - - - -

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

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

## Nankai Logic Colloquium

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 Jan Grebik from the University of Warwick. This talk is going to take place this Friday, Oct.28,  from 4 pm to 5 pm (UTC+8, Beijing time).

Title: Complexity problem in measurable combinatorics

Abstract: Given a local graph coloring problem, it is natural to ask when we can solve it in a measurable way (in various senses) on a given locally finite Borel graph. As it turned out recently, these questions are ultimately connected with the theory of local algorithms. For example, Bernshteyn showed that the existence of an efficient distributed randomized algorithm that solves a given local problem on a class of finite graphs $\mathcal{G}$ implies the existence of a $\mu$-measurable or Baire measurable solution for the same problem on Borel graphs that look locally like graphs from $\mathcal{G}$.

The most challenging and least understood setting concerns the questions about the existence of so-called Borel measurable solutions. Recently, a fascinating connection with the CSP dichotomy of Feder and Vardy in this setting was described by Thornton. Suppose for example that you want to decide when a given graph has a chromatic number at most $3$. It is a classical result that this is an NP-complete problem for finite graphs. Todorčevi ́c and Vidnyánszky showed that the analogous problem for locally finite Borel graphs is as complicated as it gets, such graphs form a ${\bf \Sigma}^1_2$-complete set. Building on this result, Thornton showed that the same holds for \emph{every} Borel version of an $\opertorname{NP}$-complete CSPs (under $\opertorname{P}\not= \operatorname{NP}$). In the first part of the talk, I will summarize these results and state open questions. In the second part, I will discuss ideas behind our recent result, with Brandt, Chang, Grunau, Rozhoň and Vidnyánszky, that states that the set of $\Delta$-regular acyclic Borel graphs that admit a proper Borel $\Delta$-coloring is ${\bf \Sigma}^1_2$-complete.

___________________________________________________________________________________________________________________________________________________

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

Title：                 The 8th Nankai Logic Colloquium -- Jan Grebik

Time：                16:00pm, Oct. 28, 2022 (Beijing Time)

Zoom Number：820 6148 1269

Passcode：         379819

_____________________________________________________________________

Best wishes,

Ming Xiao

## Wednesday seminar

Prague Set Theory Seminar
Dear all, The seminar meets on Wednesday October 26th at 11:00 in the Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building. Some news: https://www.journals.elsevier.com/topology-and-its-applications/news/dr-jan-grebik-is-the-winner-of-2022-mary-ellen-rudin-award Program: Tomasz Rzepecki -- Some topological and set-theoretic objects in model theory The plan is to present a (selective) survey of topological and descriptive set-theoretic objects that we encounter and study in pure model theory. Concepts I might touch upon include: type spaces, strong type spaces, their (logic) topology and (Borel) cardinalities, model-theoretic group components, Ellis groups and semigroups, definability and Borel definability of types and measures in stable and NIP theories. I am not assuming any familiarity with model theory. Best, David

## Barcelona Set Theory Seminar

Barcelona Logic Seminar
Dear All,
Please find attached the announcement of the next Barcelona Set Theory seminar session.

SPEAKER:   Juan P. Aguilera
TITLE: Determinacy on the Edge of Second-Order Arithmetic
DATE: Wednesday, 26 October 2022
TIME: 16:00 (CEST)
PLACE: Room B1 (UB). The Seminar can also be followed online via Zoom:

Best regards,
Joan

P.S.: If you do not wish to receive any more announcements, please send an email to bagaria@ub.edu with the text “Unsubscribe”.

Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia

Phone: +34 93 402 1609
joan.bagaria@icrea.cat
bagaria@ub.edu

## Upcoming Core Model Seminar

Carnegie Mellon Logic Seminar
TUESDAY, October 25, 2022 Core Model Seminar: 1:30 - 3 PM Eastern, Online, Derek Levinson, University of California, Los Angeles Join Zoom Meeting: https://cmu.zoom.us/j/97749733438?pwd=Yk5PcSsvekptWWxMNUhCU2pFbzA0Zz09 Meeting ID: 977 4973 3438 Passcode: 457791 TITLE: Unreachability of Pointclasses in $L(R)$, part 1 ABSTRACT: We present Hjorth's proof that there is no sequence of distinct $\Sigma^1_2$ sets of length $\delta^1_2$. Then we prove in $L(R)$ if $\Gamma$ is an inductive-like pointclass then there is no sequence of distinct $\Gamma$ sets of length $\delta_\Gamma^+$.

## (KGRC) Set Theory Seminar talk Tuesday, October 25

Kurt Godel Research Center
The KGRC welcomes as guests: Martin Hils (host: Matthias Aschenbrenner) visits the KGRC until March 31, 2023 and gives a talk on January 19, 2023 (details to be announced at a later time). Frank-Viktor Kuhlmann (host: Matthias Aschenbrenner) visits the KGRC from November 1 until January 31, 2023 and gives a talk on November 24 (details to be announced at a later time). Will Brian (host: Vera Fischer) visits the KGRC from November 1 to November 6 and gives two talks (details to be announced at a later time). Simone Ramello (host: Martin Hils) visits the KGRC from November 3 to November 8. David Chodounsky (host: Vera Fischer) visits the KGRC from December 4 until December 8 and gives a talk on December 6 (details to be announced at a later time). Jan Hubicka (host: Vera Fischer) visits the KGRC from December 5 until December 8 and gives a talk on December 6 (details to be announced at a later time). * * * Set Theory Research Seminar Kurt Gödel Research Center Tuesday, October 25 "Maximal independence and singulars" Diana Carolina Montoya Amaya (KGRC) In these talks, we will discuss the concept of maximal independent families for uncountable singular cardinals. In the first part, I will present the existing background results in the regular case from Kunen and Eskew-Fischer. In the second part, we will focus on the joint results obtained in joint work with Omer Ben-Neria: some on the existence of maximal independent families at a singular strong limit, and finally some on the possible sizes of such families. Time and Place Talk at 3:00pm in hybrid mode, in person as well as via Zoom. Universität Wien Institut für Mathematik Kolingasse 14-16 1090 Wien 1st floor Seminar room 10 Zoom: If you need the Zoom data and have not received the meeting link by the day before the talk, please contact richard.springer@univie.ac.at! (Please direct any other requests pertaining to the seminars and Zoom meeting(s) to vera.fischer@univie.ac.at.) Students at Uni Wien are required to attend in person.

## Cross-Alps Logic Seminar (speaker: Christian Rosendal)

Cross-Alps Logic Seminar
On Friday 21.10.2022 at 16:00
Christian Rosendal (University of Maryland)
will give a talk on
Amenability, optimal transport and complementation in Banach modules

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 2017 'Mathematical logic: models, sets, computability'.

## This Week in Logic at CUNY

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

- - - - Monday, Oct 17, 2022 - - - -

Rutgers Logic Seminar
Monday, October 17, 3:30pm, Rutgers University, Hill 705
Felix Weilacher (CMU)
Computable vs Descriptive Combinatorics.

Abstract: Over the past few years, many exciting connections have been found between descriptive combinatorics, where one studies classical combinatorial problems under definability constraints such as measurability or Baire-measurability, and other combinatorial settings. These include the LOCAL model of Linial used in the theory of distributed computing, and the theory of random processes. The subject of this talk is the more recent addition of computable combinatorics, where the definability constraints are, e.g. computability or recursive enumerability, to this picture. We describe several parallels between this computable setting and the Baire-measurable setting, and show how a geometric structure known as “toast” gives a systematic way of explaining them. As an application, we adapt a proof of Kierstead from the computable setting to get new upper bounds on Baire-measurable edge chromatic numbers. We also show that, for acyclic graphs, the “local problems” which can be solved Baire-measurably are exactly those which can be solved computably on so called “highly computable” graphs.

Logic and Metaphysics Workshop
Date: Monday, Oct 17, 4.15-6.15 (NY time), GC 7315

By limiting the range of the predicate variables in a second-order language one may obtain restricted versions of second-order logic such as weak second-order logic or definable subset logic. In this note we provide an infinitary strongly complete axiomatization for several systems of this kind having the range of the predicate variables as a parameter. The completeness argument uses simple techniques from the theory of Boolean algebras. The full paper is here: https://arxiv.org/abs/2207.02709.

Note: This is joint work with John Lane Bell.

- - - - Tuesday, Oct 18, 2022 - - - -

Models of Peano Arithmetic (MOPA)
Tuesday, October 18, 1:00pm
Virtual (email Victoria Gitman vgitman@nylogic.org for meeting id)

Kameryn Williams, Sam Houston University
Tightness in second-order arithmetic

Say that a theory  is tight if any two distinct extensions of  cannot be bi-interpretable. Vaguely speaking, tightness expresses a sort of maximality to the expressiveness of . Visser showed that  is tight and building on this work, Enayat showed that , second-order arithmetic with full second-order comprehension, is also tight. In this talk I will address the question of whether full logical strength of these theories of arithmetic are necessary to have tightness, focusing on subsystems of . The answer to this question is positive. If you restrict the comprehension axiom of  to only arithmetical formulae, or if you restrict it to  formulae, the resulting theory is not tight. As a specific instance, we show that if  is either the minimum omega-model of  or the minimum beta-model of - for some , then  is bi-interpretable with a carefully chosen extension  by Cohen-forcing.

This talk is about joint work with Alfredo Roque Freire.

Computational Logic Seminar
Fall Semester 2022
Tuesday, October 18
Time 2:00 - 4:00 PM
Room 3310-B
Speaker: Tudor Protopopescu, CUNY
Title: Intuitionistic Epistemic Logic

Abstract:
We outline an intuitionistic view of knowledge which maintains the original Brouwer-Heyting-Kolmogorov semantics for intuitionism and is consistent with the well-known approach that intuitionistic knowledge be regarded as the result of verification. We argue that on this view co-reflection A -> KA is valid and the factivity of knowledge holds in the form KA -> ~~A known propositions cannot be false'. We show that the traditional form of factivity KA -> A is a distinctly classical principle which, like tertium non datur A v ~A, does not hold intuitionistically, but, along with the whole of classical epistemic logic, is intuitionistically valid in its double negation form ~~(KA -> A). Within the intuitionistic epistemic framework, the knowability paradox is resolved in a constructive manner. We argue that this paradox is the result of an unwarranted classical reading of constructive principles and as such does not have the consequences for constructive foundations traditionally attributed to it.

- - - - Wednesday, Oct 19, 2022 - - - -

The New York City Category Theory Seminar
Department of Computer Science
Department of Mathematics
The Graduate Center of The City University of New York, Room 6417

Speaker:     David Ellerman, University of Ljubljana.

Date and Time:     Wednesday October 19, 2022, 7:00 - 8:30 PM.

Title:     To Interpret Quantum Mechanics:Follow the Math'': The math of QM as the linearization of the math of partitions.

Abstract: Set partitions are dual to subsets, so there is a logic of partitions dual to the Boolean logic of subsets. Partitions are the mathematical tool to describe definiteness and indefiniteness, distinctions and distinctions, as well as distinguishability and indistinguishability. There is a semi-algorithmic process or Yoga'' of linearization to transform the concepts of partition math into the corresponding vector space concepts. Then it is seen that those vector space concepts, particularly in Hilbert spaces, are the mathematical framework of quantum mechanics. (QM). This shows that those concepts, e.g., distinguishability versus indistinguishability, are the central organizing concepts in QM to describe an underlying reality of objective indefiniteness--as opposed to the classical physics and common sense view of reality as definite all the way down'' This approach thus supports what Abner Shimony called the Literal Interpretation'' of QM which interprets the formalism literally as describing objective indefiniteness and objective probabilities--as well as being complete in contrast to the other realistic interpretations such as the Bohmian, spontaneous localization, and many world interpretations which embody other variables, other equations, or other worldly ideas.

The underlying paper is forthcoming in the Foundations of Physics, and the preprint is in the ArXiv here.

- - - - Thursday, Oct 20, 2022 - - - -

- - - - Friday, Oct 21, 2022 - - - -

Set Theory Seminar
CUNY Graduate Center, Friday, October 21, 12:15pm NY time
Virtual: Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Forcing ' is -dense' from Large Cardinals - A Journey guided by the Stars

An ideal  on  is -dense if  has a dense subset of size . We prove, assuming large cardinals, that there is a semiproper forcing  so thatThis answers a question of Woodin positively. Our general strategy is based on the observation that replacing the role of  in Woodin's axiom  by  results in an axiom  which implies .
We proceed in three steps: First we define and motivate a new forcing axiom  and then modify the Asperó-Schindler proof of  to show . Finally, assuming a supercompact limit of supercompact cardinals exists, we construct a semiproper partial order forcing . This last step involves proving two new iteration theorems both of which allow for forcings killing stationary sets.

Logic Workshop
Hybrid (email Victoria Gitman for meeting id)
Friday October 21, 2:00pm-3:30pm, Room 6417
Philipp Rothmaler, CUNY
Generalized Bass modules

Over half a century ago Hyman Bass proved that all flat left modules are projective precisely when the underlying ring satisfies the descending chain condition on right principal ideals. He called such rings left perfect. Gena Puninski noticed that this can be given a model theoretic proof. Every infinite descending chain of principal right ideals gives rise to a descending chain of (pp) formulas which, in turn, gives rise to a direct limit of finitely generated projective modules that is not projective. Such a module is flat and not projective, and called a Bass module.

I demonstrate how this construction is elementary model theory and at the same time generalizes to other classes of (pp) formulas and modules, which, among other things, yields a new proof of the late Daniel Simson’s result that all left modules are Mittag-Leffler iff the ring is left pure-semisimple (which, to model theorists, means that all left modules are totally transcendental).

I will emphasize the model theoretic ideas and explain the connection with the algebraic concepts. This is part of ongoing work with Anand Pillay.

Next Week in Logic at CUNY:

- - - - Monday, Oct 24, 2022 - - - -

- - - - Tuesday, Oct 25, 2022 - - - -

- - - - Wednesday, Oct 26, 2022 - - - -

- - - - Thursday, Oct 27, 2022 - - - -

- - - - Friday, Oct 28, 2022 - - - -

Set Theory Seminar
CUNY Graduate Center, Friday, October 28, 12:15pm NY time
Virtual: Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Forcing ' is -dense' from Large Cardinals - A Journey guided by the Stars: Part II

An ideal  on  is -dense if  has a dense subset of size . We prove, assuming large cardinals, that there is a semiproper forcing  so thatThis answers a question of Woodin positively. Our general strategy is based on the observation that replacing the role of  in Woodin's axiom  by  results in an axiom  which implies .
We proceed in three steps: First we define and motivate a new forcing axiom  and then modify the Asperó-Schindler proof of  to show . Finally, assuming a supercompact limit of supercompact cardinals exists, we construct a semiproper partial order forcing . This last step involves proving two new iteration theorems both of which allow for forcings killing stationary sets.

Logic Workshop
Hybrid (email Victoria Gitman for meeting id)
Friday October 28, 2:00pm-3:30pm, Room 6417
Corey Switzer University of Vienna

- - - - Other Logic News - - - -

- - - - Web Site - - - -

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

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

## (KGRC) Set Theory Seminar talk Tuesday, October 18

Kurt Godel Research Center
The KGRC welcomes as guests: Martin Hils (host: Matthias Aschenbrenner) visits the KGRC until March 31, 2023 and gives a talk on January 19, 2023 (details to be announced at a later time). Frank-Viktor Kuhlmann (host: Matthias Aschenbrenner) visits the KGRC from November 1 until January 31, 2023 and gives a talk on November 24 (details to be announced at a later time). Will Brian (host: Vera Fischer) visits the KGRC from November 1 to November 6 and gives two talks (details to be announced at a later time). Simone Ramello (host: Martin Hils) visits the KGRC from November 3 to November 8. David Chodounsky (host: Vera Fischer) visits the KGRC from December 4 until December 8 and gives a talk on December 6 (details to be announced at a later time). Jan Hubicka (host: Vera Fischer) visits the KGRC from December 5 until December 8 and gives a talk on December 6 (details to be announced at a later time). * * * Set Theory Research Seminar Kurt Gödel Research Center Tuesday, October 18 "Maximal independence and singulars" Diana Carolina Montoya Amaya (KGRC) In these talks, we will discuss the concept of maximal independent families for uncountable singular cardinals. In the first part, I will present the existing background results in the regular case from Kunen and Eskew-Fischer. In the second part, we will focus on the joint results obtained in joint work with Omer Ben-Neria: some on the existence of maximal independent families at a singular strong limit, and finally some on the possible sizes of such families. Time and Place Talk at 3:00pm in hybrid mode, in person as well as via Zoom. Universität Wien Institut für Mathematik Kolingasse 14-16 1090 Wien 1st floor Seminar room 10 Zoom: If you need the Zoom data and have not received the meeting link by the day before the talk, please contact richard.springer@univie.ac.at! (Please direct any other requests pertaining to the seminars and Zoom meeting(s) to vera.fischer@univie.ac.at.) Students at Uni Wien are required to attend in person.

## Wednesday seminar

Prague Set Theory Seminar
Dear all, The seminar meets on Wednesday October 19th at 11:00 in the Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building. Program: Salvatore Scamperti -- Universality properties of graph homomorphism My master's thesis project was to solve a decidability problem. For this purpose, we defined a new homomorphism reduction from first-order relational structures to graphs. We will show a generalization of this construction and some consequences. Best, David

## Logic Seminar 19 Oct 2022 17:00 hrs at NUS by Abdul Basit

NUS Logic Seminar
Invitation to the Logic Seminar at the National University of Singapore Date: Wednesday, 19 Oct 2022, 17:00 hrs Place: NUS, Department of Mathematics, S17#04-05 Speaker: Abdul Basit. Title: On the shatter function of semilinear families URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html Abstract: The shatter function, a combinatorial function associated to a family of sets, is an important measure of its complexity. For example, it is related to the popular notions of VC dimension and VC density. We show that the shatter function of a semilinear family (i.e., a family definable in (R, + , <)) is asymptotic to a polynomial. This implies, in particular, that any semilinear family has integer VC density, which confirms a conjecture by Artem Chernikov. This is joint work with Tran Chieu Minh

## Logic Seminar 12 October 2022 17:00 hrs at NUS by Frank Stephan

NUS Logic Seminar
Invitation to the Logic Seminar at the National University of Singapore Date: Wednesday, 12 October 2022, 17:00 hrs Place: NUS, Department of Mathematics, S17#04-05 Speaker: Frank Stephan Title: Initial Segment Complexity for Measures URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html The talk will present selected results from the joint work of Andre Nies and Frank Stephan on complexity of measures as it is found on https://arxiv.org/abs/1902.07871

## Barcelona Set Theory Seminar (change of date)

Barcelona Logic Seminar

Dear All,
The seminar session by Christopher Turner will take place on Wednesday next week, and not this week on Thursday, as was previously announced. See the new announcement attached.
My apologies for the inconvenience caused.

SPEAKER:   Christopher Turner
TITLE: Lowenheim-Skolem-Tarski Numbers for Regularity Quantifiers
DATE: Wednesday, 19 October 2022
TIME: 16:00 (CEST)
PLACE: The IMUB Seminar room. The Seminar can also be followed online via Zoom:

Best regards,
Joan

P.S.: If you do not wish to receive any more announcements, please send an email to bagaria@ub.edu with the text “Unsubscribe”.

Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia

Phone: +34 93 402 1609
joan.bagaria@icrea.cat
bagaria@ub.edu

## Barcelona Set Theory Seminar

Barcelona Logic Seminar

El 19 juny 2022, a les 11:33, Joan Bagaria <joan.bagaria@icrea.cat> va escriure:

Dear All,

Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
Note that this week, exceptionally, the seminar will take place on Thursday, and not on Wednesday as before.

SPEAKER:   Christopher Turner
TITLE: Lowenheim-Skolem-Tarski Numbers for Regularity Quantifiers
DATE: Thursday, 13 October 2022
TIME: 16:00 (CEST)
PLACE: The IMUB Seminar room. The Seminar can also be followed online via Zoom:

Best regards,
Joan

P.S.: If you do not wish to receive any more announcements, please send an email to bagaria@ub.edu with the text “Unsubscribe”.

Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia

Phone: +34 93 402 1609
joan.bagaria@icrea.cat
bagaria@ub.edu

## This Week in Logic at CUNY

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

- - - - Monday, Oct 10, 2022 - - - -

*** Graduate Center Closed Today ***

- - - - Tuesday, Oct 11, 2022 - - - -

Models of Peano Arithmetic (MOPA)
Tuesday, October 11, 1:00pm
Virtual (email Victoria Gitman vgitman@nylogic.org for meeting id)

Fedor Pakhomov, Ghent University
How to escape Tennenbaum's theorem

We construct a theory definitionally equivalent to first-order Peano arithmetic PA and a non-standard computable model of this theory. The same technique allows us to construct a theory definitionally equivalent to Zermelo-Fraenkel set theory ZF that has a computable model. See my preprint https://arxiv.org/abs/2209.00967 for more details.

Computational Logic Seminar
Tuesday, October 11, Time 2:00 - 4:00 PM
Room 3310-B
Title:   Applying Tableaus to Observable Models and Hypertheories

Abstract: In 2020 Prof. Artemov published a paper, “Observable Models”.  I realized around then that certain kinds of tableaus provided natural tools for working with them, and wrote up some notes about it.  But Covid intervened and much that was ordinary went into storage for the duration.  Now that things are coming back, and with the recent talk on hypertheories, it seems like time to bring this work up again.

My talk will begin with a brief introduction to tableaus, for those not particularly familiar with them.  Following recent advice from a talk in the seminar itself, this will begin with classical logic.  Then we move to versions appropriate for modal logics.  We will see that we already have, in the literature, useful machinery for investigating hypertheories and their models.  The machinery has been available for a long time.  The fact that it applies with no changes says something about the naturalness of hypertheories.

The talk will consist of basics and examples of applications.  The appropriate theoretical background for tableaus has been around for years.

- - - - Wednesday, Oct 12, 2022 - - - -

- - - - Thursday, Oct 13, 2022 - - - -

- - - - Friday, Oct 14, 2022 - - - -

Set Theory Seminar
CUNY Graduate Center, Friday, October 14, 12:15pm NY time
Virtual: Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Philipp Lücke University of Barcelona

Logic Workshop
Hybrid (email Victoria Gitman for meeting id)
Friday October 14, 2:00pm-3:30pm, Room 6417
Chris Conidis, CUNY

The computability of Artin-Rees and Krull Intersection

We will explore the computational content of two related algebraic theorems, namely the Artin-Rees Lemma and Krull Intersection Theorem. In particular we will show that, while the strengths of these theorems coincide for individual rings, they become distinct in the uniform context.

Next Week in Logic at CUNY:

- - - - Monday, Oct 17, 2022 - - - -

Logic and Metaphysics Workshop
Date: Monday, Oct 17, 4.15-6.15 (NY time), GC 7315

By limiting the range of the predicate variables in a second-order language one may obtain restricted versions of second-order logic such as weak second-order logic or definable subset logic. In this note we provide an infinitary strongly complete axiomatization for several systems of this kind having the range of the predicate variables as a parameter. The completeness argument uses simple techniques from the theory of Boolean algebras. The full paper is here: https://arxiv.org/abs/2207.02709.

Note: This is joint work with John Lane Bell.

- - - - Tuesday, Oct 18, 2022 - - - -

Models of Peano Arithmetic (MOPA)
Tuesday, October 18, 1:00pm
Virtual (email Victoria Gitman vgitman@nylogic.org for meeting id)

Kameryn Williams, Sam Houston University
Tightness in second-order arithmetic

Say that a theory  is tight if any two distinct extensions of  cannot be bi-interpretable. Vaguely speaking, tightness expresses a sort of maximality to the expressiveness of . Visser showed that  is tight and building on this work, Enayat showed that , second-order arithmetic with full second-order comprehension, is also tight. In this talk I will address the question of whether full logical strength of these theories of arithmetic are necessary to have tightness, focusing on subsystems of . The answer to this question is positive. If you restrict the comprehension axiom of  to only arithmetical formulae, or if you restrict it to  formulae, the resulting theory is not tight. As a specific instance, we show that if  is either the minimum omega-model of  or the minimum beta-model of - for some , then  is bi-interpretable with a carefully chosen extension  by Cohen-forcing.

This talk is about joint work with Alfredo Roque Freire.

- - - - Wednesday, Oct 19, 2022 - - - -

- - - - Thursday, Oct 20, 2022 - - - -

- - - - Friday, Oct 21, 2022 - - - -

Logic Workshop
Hybrid (email Victoria Gitman for meeting id)
Friday October 21, 2:00pm-3:30pm, Room 6417
Philipp Rothmaler, CUNY
Generalized Bass modules

Over half a century ago Hyman Bass proved that all flat left modules are projective precisely when the underlying ring satisfies the descending chain condition on right principal ideals. He called such rings left perfect. Gena Puninski noticed that this can be given a model theoretic proof. Every infinite descending chain of principal right ideals gives rise to a descending chain of (pp) formulas which, in turn, gives rise to a direct limit of finitely generated projective modules that is not projective. Such a module is flat and not projective, and called a Bass module.

I demonstrate how this construction is elementary model theory and at the same time generalizes to other classes of (pp) formulas and modules, which, among other things, yields a new proof of the late Daniel Simson’s result that all left modules are Mittag-Leffler iff the ring is left pure-semisimple (which, to model theorists, means that all left modules are totally transcendental).

I will emphasize the model theoretic ideas and explain the connection with the algebraic concepts. This is part of ongoing work with Anand Pillay.

- - - - Other Logic News - - - -

- - - - Web Site - - - -

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

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

## Math Logic Seminar this Tuesday

Carnegie Mellon Logic Seminar
TUESDAY, October 11, 2022 Mathematical Logic Seminar: 3:30 - 4:30 PM Eastern, Online, Rehana Patel, Bentley University and Northeastern University Join Zoom Meeting: https://cmu.zoom.us/j/92655324096?pwd=VUhSSlkrdHMxbTlSYUMxYzFXM01kdz09 Meeting ID: 926 5532 4096 Passcode: 555455 TITLE: The number of ergodic models of an infinitary sentence ABSTRACT: Given an $L_{\omega_1\omega}$-sentence $\varphi$ in a countable language, we call an ergodic $S_\infty$-invariant probability measure on the Borel space of countable models of $\varphi$ (having fixed underlying set) an \emph{ergodic model} of $\varphi$. I will discuss the number of ergodic models of such a sentence $\varphi$, including the case when $\varphi$ is a Scott sentence. This is joint work with N. Ackerman, C. Freer, A. Kruckman and A. Kwiatkowska.

## Wednesday seminar

Prague Set Theory Seminar
Dear all, The seminar meets on Wednesday October 12th at 11:00 in the Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building. Program: Borisa Kuzeljevic -- Lower bounds of sets of P-points We will sketch the proof that MA(kappa) implies that each collection of P_c-points of size at most kappa which has a P_c-point as an RK upper bound also has a P_c-point as an RK lower bound. This is joint work with Dilip Raghavan and Jonathan Verner. Best, David

## (KGRC) Set Theory Research Seminar talk Tuesday, October 11

Kurt Godel Research Center
The KGRC welcomes as guests: Martin Hils (host: Matthias Aschenbrenner) visits the KGRC until March 31, 2023. Will Brian (host: Vera Fischer) visits the KGRC from November 1 to November 6 and gives two talks (details to be announced at a later time). Simone Ramello (host: Martin Hils) visits the KGRC from November 3 to November 8. * * * Set Theory Research Seminar Kurt Gödel Research Center Tuesday, October 11 "A Sacks-indestructible partion of Baire space into compact sets II" Lukas Schembecker (KGRC) Remember that maximal almost disjoint families of finitely splitting trees (a.d.f.s. families) are in one-to-one correspondence with partitions of Baire space into compact sets. In part I we saw how to construct an a.d.f.s. family which is indestructible by the product of Sacks forcing of size $\aleph_0$. In part II we strengthen the construction to get an a.d.f.s family which stays maximal after forcing with countably supported product or iteration of Sacks forcing of any length. The proof is an adaptation of the construction of a Sacks-indestructible maximal eventually different family by V. Fischer and D. Schrittesser. If time permits we give an idea how to generalize the construction to other combinatorial families, for example maximal cofinitary groups. Time and Place Talk at 3:00pm in hybrid mode, in person as well as via Zoom. Universität Wien Institut für Mathematik Kolingasse 14-16 1090 Wien 1st floor Seminar room 10 Zoom: If you need the Zoom data and have not received the meeting link by the day before the talk, please contact richard.springer@univie.ac.at! (Please direct any other requests pertaining to the seminars and Zoom meeting(s) to vera.fischer@univie.ac.at.) Students at Uni Wien are required to attend in person.

## Core Model Seminar

Carnegie Mellon Logic Seminar
Time: 1:30 to 3 PM Eastern Join Zoom Meeting: https://cmu.zoom.us/j/97749733438?pwd=Yk5PcSsvekptWWxMNUhCU2pFbzA0Zz09 Meeting ID: 977 4973 3438 Passcode: 457791 10/4 Nam Trang, Core model induction toolbox and examples, part 4 10/11 Sean Cody, Full Determinacy from Turing Determinacy over L(R) 10/18 No seminar 10/25 Derek Levinson, Unreachability of pointclasses in L(R), part 1 11/1 Derek Levinson, Unreachability of pointclasses in L(R), part 2 11/8 Sandra Müller, A stationary-tower-free proof of Sealing, part 1 11/15 Sandra Müller, A stationary-tower-free proof of Sealing, part 2 11/22 No seminar 11/29 * 12/6 * * Gabe Goldberg and/or Benny Siskind will speak on their joint work.

## This Week in Logic at CUNY

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

- - - - Monday, Oct 3, 2022 - - - -

Logic and Metaphysics Workshop
Date: Monday, Sept 19, 4.15-6.15 (NY time), GC 7315
Yale Weiss (CUNY)
Title: The best of all possible Leibnizian completeness theorems

Abstract: Leibniz developed several arithmetical interpretations of the assertoric syllogistic in a series of papers from April 1679. In this talk, I present his most mature arithmetical semantics. I show that the assertoric syllogistic can be characterized exactly not only in the full divisibility lattice, as Leibniz implicitly suggests, but in a certain four-element sublattice thereof. This refinement is also shown to be optimal in the sense that the assertoric syllogistic is not complete with respect to any smaller sublattice using Leibniz’s truth conditions.

- - - - Tuesday, Oct 4, 2022 - - - -

Models of Peano Arithmetic (MOPA)
Tuesday, October 4, 1:00pm
Virtual (email Victoria Gitman vgitman@nylogic.org for meeting id)

Pathologically defined subsets of models of

It is well known that every countable recursively saturated model of  has a full compositional truth predicate; that is, such a model is expandable to the theory . It is also well known that such a truth predicate need not be inductive, or indeed, need not satisfy even  induction. Recently, Enayat and Pakhomov showed that  induction for the truth predicate is equivalent to the principle of disjunctive correctness: the assertion that for any sequence of sentences , the disjunction  is evaluated as true if and only if there is  such that  is evaluated as true. In the absence of  induction, various pathologies can occur, including models of  for which all nonstandard length disjunctions are evaluated as true. In this talk, we classify the sets X for which there is a model of  in which X is exactly the set of those c such that the disjunctions of length c of 0 = 1 is evaluated as false. In particular, we see that X can be  if and only if  is a strong cut, and therefore the 'disjunctively trivial' models mentioned before are in fact arithmetically saturated. This is joint work (in progress) with Mateusz Łełyk.

- - - - Wednesday, Oct 5, 2022 - - - -

- - - - Thursday, Oct 6, 2022 - - - -

- - - - Friday, Oct 7, 2022 - - - -

Set Theory Seminar
CUNY Graduate Center, Friday, October 7, 11am NY time
Virtual: Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Sakae Fuchino, Kobe University

Definability of Laver-generic large cardinals and largeness of generic large cardinals with chain conditions

For a class  of posets, a cardinal  is said to be generically supercompact by  (or -gen. supercompact for short) if, for any , there are  such that, for all -generic  there are  with , and