Category Archives: Conferences

Appalachian Set Theory workshop: Benjamin Miller, January 21, 2017

Appalachian set theory

Saturday, January 21, 2017

9:30 a.m. – 6 p.m. with coffee and lunch breaks

Carnegie Mellon University

Benjamin Miller : “Applications of the open graph dichotomy”


The open graph dichotomy is a generalization of the perfect set theorem, ensuring that every open graph on an analytic set has either a countable coloring or a perfect clique. As the proof of this result is essentially the same as that of the perfect set theorem, it can be viewed as one of the very simplest descriptive set-theoretic dichotomy theorems. Nevertheless, there is an infinite-dimensional analog of the open graph dichotomy (whose proof is essentially the same) that has recently proven particularly useful in studying Borel functions, graphs, and sets of low complexity.

We will begin by stating and proving the infinite-dimensional analog of the open graph dichotomy. We will then describe how it can be used to give particularly simple proofs of several well-known facts, such as the Hurewicz dichotomies, the Jayne-Rogers theorem, and Lecomte’s characterization of the existence of countable Borel colorings of low complexity. Finally, we will turn our attention to the new result that there is a twenty-four element basis, under closed continuous embeddability, for the class of Borel functions that are not Baire class one.


2017 North American ASL Meeting: March 20-23, 2017

Conference web site

Plenary speakers
M. Aschenbrenner (UCLA)
C. Conley (Carnegie Mellon University)
I. Kalimullin (Kazan Federal Univeristy)
P. Koellner (Harvard University)
A. Medvedev (City College of New York)
A. Rinot (Bar-Ilan University)
M. Seisenberger (Swansea University)

V. Harizanov (George Washington University)

Special Sessions
Continuous model theory (Bradd Hart and Ward Henson)
Computable structure theory (Denis Hirschfeldt and Russell Miller)
Applications of set theory to topology and analysis (Michael Hrusak and Marion Scheepers)
Complexity theory and automated proofs (Sam Buss and Vijay Ganesh)
Philosophy Session (Kenneth Easwaran and Catarina Dutilh Novaes)

Program Committee
Liljana Babinkostova, Boise State University
Gregory Cherlin, Rutgers University
Barbara Csima, University of Waterloo
Antonina Kolokolova, Memorial University of Newfoundland
Justin Moore (chair), Cornell University

Local organizers
Liljana Babinkostova
Andrew Cortens
Samuel Coskey
Stephen Crowley
Randall Holmes
Alex Jackson
Marion Scheepers

A conference on the occasion of Jensen’s 80th birthday, Münster, Aug 02–04, 2017


Set theory conference


A conference on the occasion of Ronald B. Jensen‘s 80th birthday


Institut für Mathematische Logik und Grundlagenforschung, WWU Münster


Aug 02–Aug 04, 2017

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


Tentative list of speakers (incomplete):


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.


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

Invited tutorial speakers:

Invited young speakers:

Invited local speakers:

Links to previous meetings:

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)
  • Mohammad Golshani (Tehran)
  • Yair Hayut (HUJI, Jerusalem)
  • Michael Hrusak (UNAM, Mexico)
  • Péter Komjáth (ELTE, Budapest)
  • Milos Kurillic (Novi Sad)
  • 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:

Winter School, Jan 28 – Feb 4, 2017

We are pleased to announce that the registration for the Winter School in Abstract Analysis, section Set Theory & Topology is now open. The conference will take place between Jan 28th and Feb 4th 2017 in Hejnice, Czech Republic.

Tutorial speakers for this year are:

David Asperó
Joan Bagaria
Christina Brech
Andrew Marks

The conference fee is 300 EUR and covers all expenses including the bus from Prague to Hejnice and back. Accommodation will be in double rooms.

Registration deadline — December 31st, 2016

To get more information about the conference, about the fee waiver program and to register please visit our web page

If you have any questions please do not hesitate to contact us.

We hope to see you in January,

David Chodounský, Jan Starý and Jonathan Verner

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)


Appalachian Set Theory workshop: Maryanthe Malliaris, November 5, 2016

The next meeting of the Appalachian Set Theory workshop series will take place
at CMU and may be of interest to the Pittsburgh logic community.

Maryanthe Malliaris will lead a workshop on “Cofinality spectrum
problems: p, t, and model theory”.

For details please see the workshop web page at

The Appalachian Set Theory workshop series is supported by the National
Science Foundation.

BEST 2016 slides

The 23rd BEST conference was held June 15–16 in San Diego, CA.

Shehzad Ahmed – Jonsson cardinals and pcf theory
Liljana Babinkostova – A weakening of the closure operator
Kyle Beserra – On the conjugacy problem for automorphisms of countable regular trees
Erin Carmody – Killing them softly
William Chan – Every analytic equivalence relation with all Borel classes is Borel somewhere
John Clemens – Relative primeness of equivalence relations
Paul Corazza – The axiom of infinity, quantum field theory, and large cardinals
Cody Dance – Indiscernibles for $L[T_2,x]$
Natasha Dobrinen – Ramsey spaces coding universal triangle-free graphs and applications to Ramsey degrees
Paul Ellis – A Borel amalgamation property
Monroe Eskew – Rigid ideals
Daniel Hathaway – Disjoint Borel functions
Jared Holshouser – Partition properties for non-ordinal sets under the axiom of determinacy
Paul McKenney – Automorphisms of $\mathcal P(\lambda)/\mathcal I_\kappa
Kaethe Minden – Subcomplete forcing and trees
Daniel Soukup – Orientations of graphs with uncountable chromatic number
Simon Thomas – The isomorphism and bi-embeddability relations for finitely generated groups
Douglas Ulrich – A new notion of cardinality for countable first order theories
Kameryn Williams – Minimal models of Kelley-Morse set theory
Martin Zeman – Master conditions from huge embeddings

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:


Travel support is available. Requests for such should be directed to Dima Sinapova at 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.




  • 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.





  • 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)


  • 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 $[\aleph_2,\aleph_{\omega^2+3}]$.