# Set theory conference

## Aug 02–Aug 04, 2017

Organizers: Menachem Magidor (Jerusalem), Ralf Schindler (Münster), John Steel (Berkeley), W. Hugh Woodin (Harvard)

## 10th Young Set Theory Workshop, Edinburgh, July 10–14, 2017

The 10th installment of the Young Set Theory Workshop will take place July 10-14, 2017 in Edinburgh.

### Organisers

Name Institution
Brooke-Taylor, Andrew University of Leeds
Dimopoulos, Stamatis University of Bristol
Welch, Philip University of Bristol

## 6th European Set Theory Conference, Budapest, July 3–7, 2017

The 6th European Set Theory Conference (6ESTC) of the European Set Theory Society will be organized in Budapest, at the Alfréd Rényi Institute of Mathematics of the Hungarian Academy of Sciences, next year, July 3 – 7, 2017. (Date of arrival: July 2, date of departure: July 8.)

Invited speakers:
• Assaf Rinot (Bar-Ilan) tutorial, 3 lectures
• Omer Ben-Neria (Tel-Aviv-UCLA)
• Michal Doucha (Prague)
• Alan Dow (UNC Charlotte)
• Vera Fischer (U. Vienna)
• Yair Hayut (HUJI, Jerusalem)
• Michael Hrusak (UNAM, Mexico)
• Péter Komjáth (ELTE, Budapest)
• Philipp Luecke (Bonn)
• Maciej Malicki (Warsaw)
• Maryanthe Malliaris (U Chicago)
• Diego Mejia (Shizuoka)
• Ben Miller (Vienna)
• Justin Moore (Cornell)
• Itay Neeman (UCLA)
• Dillip Raghavan (Singapoore)
• Slawek Solecki (Urbana)
• Daniel Soukup (Vienna)
• Spencer Unger (UCLA)
• Toshimichi Usuba (Tokio, Waseda U)

Local Organizing Committee:
L. Soukup (chair), M. Elekes (secretary), I. Juhász, V. Kiss, G. Sági, D. Sziráki, Z. Vidnyánszky.

Program Committee:
I. Juhász (chair, Budapest), T. Bartoszynski (Washington, DC), M. Džamonja (Norwich), S. D. Friedman (Vienna), W. Kubiś (Kielce and Prague), M. Magidor (TBC, Jerusalem), H. Mildenberger (Freiburg).

If you are interested in attending this meeting, we kindly ask you to fill out the following very short form:
https://goo.gl/Fl5ssU

## Set Theory and its Applications in Topology, September 11-16, 2016

The meeting took place in Oaxaca, Mexico. The slides may be found below.

 08:45 – 09:00 Introduction and Welcome (Conference Room San Felipe) 09:00 – 10:00 Alan Dow: The even numbered problems (Conference Room San Felipe) 10:00 – 10:30 Rodrigo Jesus Hernandez Gutierrez: Spaces discretely generated at infinity (Conference Room San Felipe) 10:30 – 11:00 Coffee Break (Conference Room San Felipe) 11:00 – 11:30 Isván Juhász: Lindelöf spaces of countable pseudocharacter (Conference Room San Felipe) 11:30 – 12:00 Juris Steprans: PID and universal graphs (Conference Room San Felipe) 13:20 – 13:30 Group Photo (Hotel Hacienda Los Laureles) 13:30 – 15:00 Lunch (Restaurant Hotel Hacienda Los Laureles) 15:00 – 16:00 Itay Neeman: Forcing one instance of the Moore-Todorcevic principle (Conference Room San Felipe) 16:00 – 16:30 Coffee Break (Conference Room San Felipe) 16:30 – 17:00 James Cummings: Dowker and super-Dowker filters (Conference Room San Felipe) 17:00 – 17:30 Assaf Rinot: The $\omega_2$-Souslin problem (Conference Room San Felipe) 19:00 – 21:00 Dinner (Restaurant Hotel Hacienda Los Laureles)
Tuesday, September 13
07:30 – 09:00 Breakfast (Restaurant at your assigned hotel)
09:00 – 10:00 Christina Brech: Bases of Homogeneous families bellow the first Mahlo cardinal (Conference Room San Felipe)
10:30 – 11:00 Coffee Break (Conference Room San Felipe)
11:00 – 11:30 Piotr Koszmider: A non-commutative Mrówka’s $\Psi$-space (Conference Room San Felipe)
11:30 – 12:00 Asger Tornquist: Invariant descriptive set theory and almost disjointness modulo an ideal (Conference Room San Felipe)
13:30 – 15:00 Lunch (Restaurant Hotel Hacienda Los Laureles)
15:00 – 16:00 Alexander Shibakov: Sequential groups: large and small (Conference Room San Felipe)
16:00 – 16:30 Coffee Break (Conference Room San Felipe)
16:30 – 17:00 Jindrich Zapletal: Strong measure zero sets in Polish groups (Conference Room San Felipe)
17:00 – 17:30 Marcin Sabok: On hyperfiniteness of boundary actions of hyperbolic groups (Conference Room San Felipe)
19:00 – 21:00 Dinner (Restaurant Hotel Hacienda Los Laureles)
Wednesday, September 14
07:30 – 09:00 Breakfast (Restaurant at your assigned hotel)
09:00 – 09:30 Joerg Brendle: Q (Conference Room San Felipe)
09:30 – 10:00 Dilip Raghavan: More on the density zero ideal (Conference Room San Felipe)
10:00 – 10:30 Osvaldo Guzmán: Combinatorial properties of MAD families (Conference Room San Felipe)
10:30 – 11:00 Coffee Break (Conference Room San Felipe)
11:00 – 11:30 Victor Torres-Perez: Constructions with oppositions: Cardinal invariants and games (Conference Room San Felipe)
11:30 – 12:00 David Fernández Bretón: Strong failures of higher analogs of Hindman’s theorem (Conference Room San Felipe)
12:00 – 12:30 Natasha Dobrinen: Topological Ramsey spaces in some creature forcings (Conference Room San Felipe)
12:30 – 13:30 Lunch (Restaurant Hotel Hacienda Los Laureles)
13:30 – 17:30 Free Afternoon (Oaxaca)
19:00 – 21:00 Dinner (Restaurant Hotel Hacienda Los Laureles)
Thursday, September 15
07:30 – 09:00 Breakfast (Restaurant at your assigned hotel)
09:00 – 10:00 Slawomir Solecki: Monoid actions on left-topological compact semigroups (Conference Room San Felipe)
10:30 – 11:00 Coffee Break (Conference Room San Felipe)
11:00 – 11:30 Aleksandra Kwiatkowska: The Ramsey degree of the pre-pseudoarc (Conference Room San Felipe)
11:30 – 12:00 Dana Bartosova: Ultrafilter combinatorics in topological dynamics (Conference Room San Felipe)
13:30 – 15:00 Lunch (Restaurant Hotel Hacienda Los Laureles)
15:00 – 16:00 Jan van Mill: Erdős spaces (Conference Room San Felipe)
16:00 – 16:30 Coffee Break (Conference Room San Felipe)
16:30 – 17:00 Anush Tserunyan: Topological dimension and Baire category (Conference Room San Felipe)
17:00 – 17:30 Yinhe Peng: Weak network and the basis problem (Conference Room San Felipe)
19:00 – 21:00 Dinner (Restaurant Hotel Hacienda Los Laureles)
Friday, September 16
07:30 – 09:00 Breakfast (Restaurant at your assigned hotel)
09:00 – 09:30 Jeffrey Bergfalk: Walks… (Conference Room San Felipe)
09:30 – 10:00 Iian Smythe: A local Ramsey theory for block sequences (Conference Room San Felipe)
10:00 – 10:30 Noé de Rancourt: Ramsey theory with and without the pigeonhole principle (Conference Room San Felipe)
10:30 – 11:00 Coffee Break (Conference Room San Felipe)
11:00 – 11:30 Claribet Piña: Topological partition relations for $\omega^2$ (Conference Room San Felipe)
11:30 – 12:00 Carlos Uzcategui: Bases and selectors for cofinal families of countable sets (Conference Room San Felipe)
12:00 – 12:30 Carlos Di Prisco: Graphs on the Cantor set (Conference Room San Felipe)
12:30 – 14:30 Lunch (Restaurant Hotel Hacienda Los Laureles)

## Set theory workshop at UIC, October 20-23, 2016

Set theory workshop

The workshop will be held at the University of Illinois at Chicago on October 20-23. Topic will cover forcing, large cardinals, applications of set theory. We will have three tutorials from leading experts and several talks by younger researchers.

The invited speakers are:
Tutorials:

Talks:

Travel support is available. Requests for such should be directed to Dima Sinapova at sinapova@math.uic.edu. Such requests will be handled on a case-by-case basis within the limits of the budget. Graduate students, young researchers, female mathematicians and members of underrepresented groups are particularly encouraged to apply.

Abstracts

### Tutorials:

• Matt Foreman (UC Irvine)Applications of descriptive set theory to classical dynamical systems

In 1932 von Neumann proposed the project of classifying smooth measure preserving transformations. As part of the project he raised the question of whether every ergodic measure preserving transformation of the unit interval is isomorphic to a diffeomorphism of a manifold.
Despite deep progress on both questions, they remained open until recently. The lecture presents joint work with B. Weiss that shows that the classification problem is impossible to solve–because the associated equivalence relation is not Borel (and moreover is strictly more complicated than any $S^\infty$-action). Along the way the authors made progress on the second problem, by showing that a quasi-generic class of transformations can be realized as diffeomorphisms of the 2-torus. This class is the source of the complexity of the classification problem.

• Menachem Magidor (Jerulasem)Compactness for chromatic numbers and other cardinal sins

A compactness principle is a statement of the form: If every small substructure of a given structure has a certian property, then the whole structure has this property. In this tutorial we shall deal with the property “The graph G has chromatic number <= \kappa”. We shall connect this property with other set theoretical principles, like reflection of stationary sets, give some consistency results using large cardinals and list some interesting open problems.

• Justin Moore (Cornell)Iterated forcing and the Continuum Hypothesis

One of the great successes in set theory in the 1970s and 80s has been the isolation of an optimal hypothesis for iterating forcings while preserving uncountablity. It turns out that while there is a well developed theory of iterating forcings which do not introduce new reals, this theory is necessarily more ad hoc in nature. This tutorial will discuss Shelah’s preservation theorems for not adding reals as well as recently discovered examples which illustrate that these results are, in some sense, sharp.

### Talks:

• Omer Ben Neria (UCLA)The distance between HOD and V

The pursuit of better understanding the universe of set theory V motivated an extensive study of definable inner models M whose goal is to serve as good approximations to V. A common property of these inner models is that they are contained in HOD, the universe of hereditarily ordinal definable sets. Motivated by the question of how “close” HOD is to V, we consider various related forcing methods and survey known and new results. This is a joint work with Spencer Unger.

• Sherwood Hachtman (UIC)Forcing analytic determinacy

The earliest-known tight connection between determinacy and large cardinals is the theorem of Martin and Harrington that $\Sigma^1_1$ determinacy is equivalent to the existence of $0^{\#}$. All known proofs of the forward implication go through Jensen’s Covering Lemma; Harrington asked whether the theorem can be proved just in second-order arithmetic. We discuss progress on Harrington’s question, building in particular on work of Cheng and Schindler showing that the standard proofs of Harrington’s theorem cannot be carried out in any system substantially weaker than fourth-order arithmetic. We also describe a connection with the proper class games recently described by Gitman and Hamkins.

• Maxwell Levine (UIC)Weak Squares and Very Good Scales

The combinatorial properties of large cardinals tend to clash with those satisfied by G\”odel’s constructible universe, especially the square property (denoted $\square_\kappa$) isolated by Jensen in the seventies. Strong cardinal axioms refute the existence of square, but it is possible with some fine-tuning to produce models that exhibit some large cardinal properties together with weakenings of square. In this talk we will exhibit some results along these lines and will outline the techniques used to produce them.

• Kostyantyn Slutskyy (UIC)Space decomposition techniques in Borel dynamics

In recent years a substantial progress has been achieved in the field of Borel dynamics. A part of this progress is due to the development of space decomposition methods. The goal of the talk is to make an overview of the old and new results that have been proved along this path. In particular, we will discuss in various degrees of details the following: Dougherty-Jackson-Kechris classification of hyperfinite Borel equivalence relations, Multi-Tower Rokhlin Lemma for Borel automorphisms and regular cross sections of Borel flows, Lebesgue orbit equivalence of multidimensional flows, and Hochman’s proof of existence of finite generators for compressible automorphisms.

• Nam Trang (UC Irvine)Compactness of $\omega_1$

We investigate various aspects of compactness of $\omega_1$ under ZF + DC. We say that $\omega_1$ is X-supercompact if there is a normal, fine, countably complete nonprincipal measure on $\mathcal P_{\omega_1}(X)$ (in the sense of Solovay). We say $\omega_1$ is X-strongly compact if there is a fine, countably complete nonprincipal measure on $\mathcal P_{\omega_1}(X)$. We discuss various results in constructing and analyzing canonical models of $AD^+$ + $\omega_1$ is (X)-supercompact. We also discuss whether the theories “$\omega_1$ is X-supercompact” and “$\omega_1$ is X-strongly compact” can be equiconsistent for various X.

• Anush Tserunyan (UIUC)
TBA

• Spencer Unger (UCLA)The poor man’s tree property

Motivated by producing a model where no regular cardinal greater than $\aleph_1$ carries a special Aronszajn tree, we prove that from large cardinals it is consistent that $\aleph_{\omega^2}$ is strong limit and there are no special Aronszajn trees on any regular cardinal in the interval $[\aleph_2,\aleph_{\omega^2+3}]$.

## Infinite Combinatorics and Forcing Theory, Kyoto, November 28 – December 1, 2016

RIMS Workshop on Infinite Combinatorics and Forcing Theory
November 28 – December 1, 2016
at the Research Institute for Mathematical Sciences (RIMS), Kyoto University

The workshop website:
http://www.ipc.shizuoka.ac.jp/~styorio/rims16/index.html

Tutorial speakers:

Speakers:

RIMS workshop is held in almost every year at the RIMS, Kyoto University in Kyoto city.
The topic of the workshop is set theory and its applications.
Its goal is to bring together researchers in these areas from Japan
The program will feature two tutorials.
Additionally, we expect many talks, in particular by junior
participants, both from Japan and abroad.

Participants are encouraged to contribute with a talk.
If you are interested, please send an email to the organizer:
Teruyuki Yorioka (Shizuoka University)
styorio@ipc.shizuoka.ac.jp

Organizer:
Teruyuki Yorioka (Shizuoka University)

Scientific Committee:
Joerg Brendle (Kobe University)
Diego A. Mejía (Shizuoka University)

## 2016 Graduate summer school in set theory, Irvine, July 25 – August 5 2016

A graduate summer school in set theory will be held July 25 – August 5 2016 at the University of California Irvine.

The subject of the summer school will be singular cardinal combinatorics, with a focus on PCF theory. The school will begin with a thorough treatment of PCF and related topics in combinatorial set theory, including club guessing and approachability. After this the school will treat interactions between PCF and other areas of set theory (including for example large cardinals, forcing axioms, reflection principles and squares).

The instructors will include James Cummings (CMU) and Christopher Lambie-Hanson (Hebrew University of Jerusalem). Lectures will be held Monday-Friday in each of the weeks July 25-29 and August 1-5. Each day will include two 90-minute lectures and two 90-minute discussion periods.

Participants will be housed in student housing on the Irvine campus. The school will fully support US citizens and permanent residents: this includes housing, meals, and travel costs (from US cities using US carriers).

If you are a graduate student and are interested in attending the summer school, please write to 2016gsst@gmail.com with a short statement about your background in set theory and your interest in attending.

The web page for the summer school is

http://www.math.cmu.edu/users/jcumming/summer_school/

This summer school is supported by the National Science Foundation grant DMS-1044150 as part of the program EMSW21-RTG: Logic in Southern California.

## Camilo Enrique Argoty lecture series

Camilo Enrique Argoty from the Sergio Arboleda University in Bogota, Colombia visits Institute for Research in Fundamental Sciences in Tehran, Iran between May 4 and May 12, 2016 for giving some lectures on the model theory of Hilbert spaces. This mini course gives a panorama of model theory of Hilbert spaces in two frameworks: continuous first order logic and abstract elementary classes. The program of the sessions is as follows:

First session: Basic Hilbert space Model Theoretic Properties: Categoricity, stability, characterization of types, quantifier elimination, characterization of non-forking
Second session: Hilbert spaces with a normal operator: Elementary equivalence, $\aleph_0$ categoricity up to perturbations, types as spectral measures, quantifier elimination, non-forking, orthogonality and domination.
Third session: Hilbert spaces with a closed unbounded self-

adjoint operator: Metric abstract elementary classes (MAEC’s); a

n
MAEC

for a Hilbert space with a closed unbounded self-adjoint operator; continuous first order elementary equivalence; types as spectral measures; non-forking, orthogonality and domination.

Fourth session: Model theory of representations of C*-algebras: Elementary equivalence; $\aleph_0$ categoricity up to perturbations; the generic representation of a C*-algebra; homoeomorphism of the stone space and quasi-state space and quantifier elimination; Non-forking, orthogonality and domination.
Fifth session:  Further work: Elementary equivalence in *-representations of *-algebras

There is a program in Italy to hire in an Italian university of their choice young researchers (of any nationality) with a position which (after three years) can evolve into that of an associate professor.

The program is very competitive (24 positions per year in all academic fields) and is reserved to researchers who have spent the last three years in research positions out of Italy. However in the past editions two logicians won one of these grants (Motto Ros and Dimonte), so there is room for logicians to find their way to success.
The relevant webpages for the call are:
and

## Appalachian Set Theory workshop: Itay Neeman, April 9, 2016

Appalachian set theory

# Itay Neeman : “Forcing with countable conditions”

## Description

The workshop will cover forcing techniques used in the proof that consistently every two ℵ2-dense real order types are isomorphic.

The question is related to the quest for higher analogues for applications of the proper forcing axiom (PFA). It was raised by Baumgartner in the early 1970s, when he proved the analogous result at ℵ1. Baumgartner’s result at ℵ1 is a central consequence of PFA (though it precedes the formulation of PFA by almost a decade) and moreover the methods of his proof have been instrumental for other key applications of PFA.

Projected topics include countable reflection of clubs, sparse sets, and iteration theory for countably closed forcing with side conditions.