## Peter Holy: The exact strength of the class forcing theorem

Monday, October 23, 2017, 16.30
Seminar room 0.008, Mathematical Institute, University of Bonn

Speaker: Peter Holy (Universität Bonn)

Title: The exact strength of the class forcing theorem

Abstract:

We consider second order set theories, that have as objects both sets and classes, and the role of the class forcing theorem, that is the forcing theorem for all notions of class forcing, within this range of theories. While Kelley-Morse class theory (KM) proves the class forcing theorem, its failure is consistent with the axioms of Gödel-Bernays set theory (GBC). We show that the class forcing theorem is equivalent, over GBC, to the principle of elementary transfinite (class) recursions of length Ord, and to the existence of various kinds of truth predicates. This is joint work with Victoria Gitman, Joel Hamkins, Philipp Schlicht and Kameryn Williams.

## Vahagn Aslanyan: Ax-Schanuel and related problems

Mathematical logic seminar – Oct 24 2017
Time:     3:30pm – 4:30 pm

Room:     Wean Hall 8220

Speaker:         Vahagn Aslanyan
Department of Mathematical Sciences
CMU

Title:     Ax-Schanuel and related problems

Abstract:

Ax proved a functional analogue of Schanuel’s conjecture in 1971. I will show how one can use it to axiomatise the first-order theory of the exponential differential equation in analogy with Zilber’s pseudo-exponentiation. Then I will discuss the possibility of Ax-Schanuel type results for other functions (differential equations), and some related problems. If time permits, I will show how Ax-Schanuel can be applied to prove a weak version of the Conjecture on Intersections with Tori.

## Jinglun Cai: C(n)-Ultrastrong Cardinals

BARCELONA SET THEORY SEMINAR

Date: Wednesday 25 October 2017

Time: 16:00

Place: Room S-3
Department of Mathematics & Computer Science
University of Barcelona
Gran Via de les Corts Catalanes 585
08007 Barcelona

Speaker: Jinglun Cai  (Universitat de Barcelona)

Title: C(n)-Ultrastrong Cardinals

Abstract: see attached.

## David J. Fernández Bretón: Higher degree versions of the Central Sets Theorem, II

Thursday, October 26, 2017, from 4 to 5:30pm
East Hall, room 3096

Speaker: David J. Fernández Bretón (University of Michigan)

Title: Higher degree versions of the Central Sets Theorem, II

Abstract:

The Central Sets Theorem is a Ramsey-theoretic result due to Furstenberg, from 1981, and multiple generalizations of it (in a variety of different directions) have been proved afterwards (to the best of my knowledge, the currently most general statement is due to De, Hindman and Strauss in 2008, but there are also many relevant results due to Bergelson). This is the second of a series of two talks, where we will explain how to interpret the Central Sets Theorem as a statement about linear polynomials in a polynomial ring with countably many variables, and prove a couple of natural generalizations involving polynomials of higher degree. The main tool that we use in our proof is the algebra of the Cech–Stone compactification (that is, these are “ultrafilter proofs”).

## Bruno Braga: Coarse embeddings into superstable spaces

Place: Fields Institute (Room 210)

Date: October 20 , 2017 (13:30-15:00)

Speaker: Bruno Braga

Title:Coarse embeddings into superstable spaces

Abstract: In 1981, J. Krivine and B. Maurey introduced the definition of stable  Banach spaces, and, in 1983, Y. Raynaud introduced the notion of superstability and studied uniform embeddings of Banach spaces into superstable Banach spaces. In this talk, we will talk about coarse embeddings into superstable spaces. This is a joint work with Andrew Swift.

## Jan Grebik: Borel selectors of Borel ideals (continued)

Dear all,

The seminar meets on Wednesday October 25th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.

Program: Jan Grebik — Borel selectors of Borel ideals (continued)
We present a result that there is an F_sigma ideal without Borel
selector and deduce that Galvin’s lemma does not have a “Borel proof.”
We also show that Nash-Williams theorem has a “Borel proof” and
therefore Galvin’s lemma is intrinsically more complex than
Nash-Williams theorem.

Best,
David

## Monroe Eskew: Global Chang’s Conjecture

KGRC Research seminar on 2017-10-19 at 4pm.

Speaker: Monroe Eskew (KGRC)

Abstract: Instances of Chang’s Conjecture (CC) can be seen as a generalization of the Loweheim-Skolem Theorem to a logic in between those the first and second order. Foreman asked how far the analogy with Lowenheim-Skolem can go, specifically whether a global version of CC is consistent. In joint work with Yair Hayut, the speaker answered Foreman’s question affirmatively, and in the process lowered the known upper bounds on consistency strength for many instances of CC. We will discuss the results, as well as some barriers that singular cardinal combinatorics impose on the possibility of a stronger global CC.

## The 14th International Workshop on Set Theory in Luminy, October 9-13, 2017

14th International Workshop in Set Theory
October 9 – 13 2017
CIRM, Luminy, Marseille

Organizers: M. Dzamonja, M. Magidor, B. Velickovic, H. Woodin

MONDAY, October 9 2017

MORNING

9:20 – 9:50 A. APTER (CUNY, Baruch College and the Graduate Center, NY, USA)
Tall, strong, and strongly compact cardinals

10:00-10:30 V. FISCHER (Kurt Gödel Research Center, University of Vienna)
Bounding, splitting and almost disjointness can be quite different

10:30 – 11:00 Coffee break

11:00 – 11:50 R. SCHINDLER (Muenster University, Germany)
Varsovian models with more Woodin cardinals

12:00 – 12:30 P. WELCH (University of Bristol, UK)
Characterizing the Hartig quantifier model

AFTERNOON

16:00 – 16:30 M. ZEMAN. (University of California, Irvine, USA)
An iteration strategy for the model $K^c$.

16:40 – 17:10 H. SAKAI (Kobe University, Japan)
On models generated by uncountable indiscernible sequences

17:10 – 17:40 Coffee break

17:40 – 18:30 J. BRENDLE (Kobe University, Japan)
Rearrangements and subseries

18:40 – 19:10 D. LECOMTE (Université de Pierre et Marie Curie, Paris)
Borel complexity of equivalence relations

TUESDAY, October 10 2017

MORNING

9:00 – 9:50 J. D. HAMKINS (City University of New York, USA)
The hierarchy of second-order set theories between GBC and KM and beyond

10:00 – 10:30 J. KRUEGER (University of North Texas, Denton, TX, USA)
Club isomorphisms on higher Aronszajn trees

10:30 – 11:10 Coffee break

11:10 – 12:00 L. FONTANELLA (Université d’Aix-Marseille, France)
From forcing models to realizability models

AFTERNOON

16:00 – 16:50 A. RINOT (Bar-Ilan University, Israel)
Distributive Aronszajn trees

16:50 – 17:20 Coffee break

17:20 – 17:50 M. FOREMAN (UC Irvine, CA, USA)
An independence result involving diffeomorphisms of the torus

18:00 – 18:30 L. ZDOMSKYY (TU Wien, Austria)
Vitali-Hahn-Saks property of Boolean algebras in forcing extensions

18:40 – 19:10 T. TSANKOV (IMJ-PRG, University of Paris Diderot, Paris, France)
Universal minimal flows relative to a URS

WEDNESDAY, October 11 2017

MORNING

9:00 – 9:30 J. MOORE (Cornell University, Ithaca, NY, USA)
On non sigma-scattered linear orders

9:40 – 10:30 L. MOTTO ROS (University of Torino, Italy)
Generalized descriptive set theory and classification

10:30 – 11:00 Coffee break

11:00 – 11:50 P. KOSZMIDER (IMPAN, Warsaw, Poland)
Noncommutative thin-tall algebras

12:00 – 12:30 D. SOUKUP ((KGRC, University of Vienna, Austria)
Monochromatic sumsets for colorings of R

AFTERNOON – Excursion to Marseille and dinner at the restaurant Les Arcenaulx

THURSDAY, October 12 2017

MORNING

9:00 – 9:50 D. SINAPOVA (Univ. of Illinois, Chicago, IL, USA)
Prikry type forcing and combinatorial principles

10:00 – 10:30 O. BEN NERIA (UC Los Angeles, CA, USA)
Singular stationarity

10:30 – 11.10 Coffee break

11:10 – 12:00 S. GAO (University of North Texas, Denton, TX, USA)
Non-Archimedean Abelian Polish Groups and Their Actions

AFTERNOON

16:00 – 16:50 N. DOBRINEN (University of Denver, CO, USA)
The universal homogeneous triangle-free graph has finite big Ramsey degrees

17:00 – 17:30 S. THOMAS (Rutgers University, New Brunswick, USA)
The isomorphism and bi-embeddability relation for countable torsion abelian groups

17:30 – 17:50 Coffee Break

17:50 – 18:40 M. VIALE (University of Torino, Italy)
An overview on category forcing

18:50-19:20 P. SCHLICHT (Univ. Bonn, Germany)
The Hurewicz dichotomy for definable subsets of generalized Baire spaces

FRIDAY, October 13 2017

MORNING

9:00 – 9:30 A. VIGNATI (IMJ-PRG, University of Paris Diderot, Paris, France)
Set theory and C*-algebras: automorphisms of continuous quotients

9:40 – 10:30 S. UNGER (Tel Aviv University, Israel)
Successives failures of approachability

10:30 – 11:00 Coffee break

11:10 – 12:00 H. MILDENBERGER (Albert Ludwigs Univ. Freiburg, Germany)
Local Ramsey Spaces in Matet Forcing Extensions

12:00 – 12:30 I. NEEMAN (UC, Los Angeles, USA)
Embedding theorem and regularity properties under AD^+

## Vahagn Aslanyan: Schanuel’s conjecture, pseudo-exponentiation, and Ax’s theorem

Mathematical logic seminar – Oct 17 2017

Time:     3:30pm – 4:30 pm

Room:     Wean Hall 8220

Speaker:         Vahagn Aslanyan
Department of Mathematical Sciences
CMU

Title:     Schanuel’s conjecture, pseudo-exponentiation, and Ax’s theorem

Abstract:

Schanuel’s conjecture captures the transcendence properties of the complex exponential function, and is considered out of reach. An interesting, novel approach to it was given by Zilber which led to the construction of pseudo-exponentiation. This gave rise to more conjectures related to Schanuel’s conjecture and the complex exponential field C_exp. One of those, known as Zilber-Pink, is purely number theoretic and generalises many known conjectures (and results) in diophantine geometry such as Mordell-Lang and Andree-Oort. I will describe Zilber’s construction and the Zilber-Pink conjecture. If time permits, I will also discuss a functional analogue of Schanuel’s conjecture proven by Ax in 1971.

## MAMLS Logic Friday, New York, October 27, 2017

Mid-Atlantic Mathematical Logic Seminar

October 27, 2017

Room 6417

MAMLS Logic Friday is a one-day logic meeting taking place at the CUNY Graduate Center with the support of the National Science Foundation. It will feature talks in set theory, computability theory, and model theory.

While graduate students, young researchers, female mathematicians and members of underrepresented groups are particularly encouraged to apply for travel support, it should be stressed that any participants without their own sources of funding are eligible to apply. Requests will be handled on a case-by-case basis within the limits of the budget. To apply for travel support or to find out more information, please contact Victoria Gitman (vgitman@nylogic.org).

Information about hotels can be found here.

Speakers

Schedule

9:00-9:30
Breakfast (Math Lounge 4214)

Morning Session

9:30-10:15
Ivo Herzog
The Logic of Positive Primitive Formulae
We will discuss the structure of positive primitive formulae in the language of modules over a ring R. This structure includes two cubical lattices related by the Prest dual. We place particular emphasis on the resemblance of positive primitive logic to quantum logic and von Neumann’s work on the coordinatization of complemented modular lattices. For a ring (R,*) with involution, this gives rise to a quantum logic coordinatized by a *-regular ring obtained by adjusting a classical construction of Olivier for commutative rings.

10:30-11:15
Tim McNicholl
Computable metric structure theory
I will begin by reviewing the evolution of computable structure theory beginning with its origins in the work of van der Waerden on constructive algebra. I will then discuss recent work on extending the computable structures program to metric structures by means of the framework of computable analysis. I will focus on Banach spaces, and in particular recent results on computable categoricity and degrees of categoricity of

spaces. The solutions of some of the resulting problems involve am interesting blend of methods from functional analysis and classical computability theory.

Lunch

11:30-12:30
Lunch Break

Afternoon Session

12:45-1:30
Chris Lambie-Hanson
Reflections on graph coloring
In 1951, de Bruijn and Erdős published a compactness theorem for graphs with finite chromatic number, proving that, if is a graph, is a natural number, and all finite subgraphs of have chromatic number at most , then has chromatic number at most . Since then, infinitary generalizations of this theorem, for the chromatic number as well as the coloring number of graphs, have attracted much attention. In this talk, we will briefly review some of the historical highlights in this area and then present some new work. These results show that the coloring number can exhibit only a limited amount of incompactness, while large amounts of incompactness for the chromatic number are implied by relatively weak hypotheses. This indicates that the coloring number and chromatic number behave quite differently with respect tocompactness and illustrates the difficulty involved in obtaining infinitary analogues of the de Bruijn-Erdős result at infinite, accessible cardinals. This is joint work with Assaf Rinot.

1:45-2:30
Matthew Harrison-Trainor
Some Computable Structure Theory of Finitely Generated Structures
Every countable structure has a sentence of infinitary logic, called a Scott sentence, which describes it up to isomorphism among countable structures. We can characterize the complexity of a structure by the complexity of the simplest description of that structure. A finitely generated structure always has a

description. We show that there is a finitely generated group which has no simpler description. The proof of this leads us to talk about notions of universality for finitely generated structures. Finitely generated groups are universal, but finitely generated fields are not. By this, we mean that for every finitely generated structure, there is a finitely generated group which has the same computability-theoretic properties; but the same is not true for finitely generated fields. We apply the results of this investigation to pseudo Scott sentences.

2:45-3:30
Stamatis Dimopoulos
Woodin-for-strong-compactness cardinals, a new identity crisis
Woodin and Vopěnka cardinals are established notions in the large cardinal hierarchy and despite being defined in different context, they proved to be very similar. In fact, Vopěnka cardinals are obtained by replacing a strongness clause in the definition of Woodinness by a supercompactness clause. Since strong compactness is an intermediate large cardinal notion between strongness and supercompactness, it is natural to consider a “Woodinised” version of it. In this talk, we give the definition of this new type of large cardinal, called Woodin for strong compactness, and will present some results about them. The highlight is that the analogue of Magidor’s “identity crisis” theorem for the first strongly compact holds for these cardinals too: the first Woodin for strong compactness cardinal can consistently be the first Woodin or the first Vopěnka cardinal.