2013 ESI Set Theory

Forcing, Large Cardinals and Descriptive Set Theory

Forcing, Large Cardinals and Descriptive Set Theory is a six-week Thematic Programme (invitation only) at the Erwin Schrödinger International Institute for Mathematical Physics (ESI).

Committee:
    S. D. Friedman (U. Wien), M. Goldstern (TU Wien), A. Kechris (Caltech, USA), J. Kellner (U. Wien), W. H. Woodin (UC Berkeley, USA)
Dates:
    September 9 - October 18, 2013
Venue:
    Week 1: KGRC
    Weeks 2-6: ESI

Weeks 1-3 (Sep9-27) will concentrate on Forcing and Large Cardinals; weeks 4-6 (Sep30-Oct18) on Descriptive set theory. The Programme will include two workshops:

Forcing and Large Cardinals (FLC) - week 3, September 23-27
Descriptive Set Theory (DST) - (week 4, September 30 - October 4

The field experienced dramatic developments in recent years.

A new approach to consistency lower bounds in set theory, which one might refer to as quasi lower bounds, emerged initially from work of Neeman and has been developed further by Friedman-Holy, Sakai and Velickovic and especially Viale-Weiß. Instead of showing that large cardinals are definitively required for set-theoretic properties, one shows that they are required to obtain those properties by the method of forcing, given certain hypotheses on the ground model and the type of forcing used.

A second development is in the application of descriptive set theory to the study of C*-algebras: Farah showed that it is consistent that all automorphisms of the Calkin algebra are inner, and further joint work of his with Toms, Törnquist and others has recently produced dramatic results regarding the unclassifiability of separable C*-algebras. A striking interaction of set theory with ergodic theory is Foreman-Weiss's recent anti-classification theorem for measure-preserving diffeomorphisms of the torus.

In pure descriptive set theory, the exciting ramifications of Ben Miller's recent work reducing numerous dichotomy theorems to variants of the Kechris-Solecki-Todorcevic graph dichotomy are still being worked out. And recently, Friedman-Hyttinen-Kulikov have discovered a connection between higher descriptive set theory and Shelah's classification of first-order theories; many interesting problems remain both on the set-theoretic and model-theoretic sides of this new theory.

The ESI Programme will bring together well established research leaders of the field as well as young postdocs and PhD students to work on these (and other) developments.

Venue

The conference will take place at the Erwin Schrödinger Institue (ESI), Boltzmanngasse 9, 1090 Wien; second floor (= top floor, 2 floors above the ground; sorry, no elevator).

Participants

We expect the following participants:
(Week 1: Sep 9-13, 2: Sep 16-20, 3: Sep 23-27, 4: Sep30-Oct4, 5: Oct 7-11, 6: Oct 14-18.)

This list (and the dates for individual participants) is only preliminary.

International Participants

Name	Affiliation	Week(s)
Name	Affiliation	1	2	3	4	5	6
Hiroshi Ando	IHES, France				X
Alessandro Andretta	University of Torino, Italy			X
Giorgio Audrito	University of Torino, Italy			X
Joan Bagaria	University of Barcelona, Spain			X
Dana Bartosova	University of Toronto, Canada				X
Tomek Bartoszynski	National Science Foundation, USA				X	X
Kostas Beros	University of Wisconsin, USA				X
Piotr Borodulin-Nadzieja	University of Wroclaw, Poland			X
Riccardo Camerlo	Politecnico di Torino, Italy				X
David Chodounsky	Academy of Sciences of the Czech Republic			X
James Cummings	Carnegie-Mellon University, USA		X	X
Udayan Darji	University of Louisville, Kentucky, USA				X
Gabriel Debs	University of Le Havre and Institut Mathematique de Jussieu, France				X
Pandelis Dodos	University of Athens, Greece				X
Gregor Dolinar	University of Ljubljana, Slovenia			X
Ohad Drucker	The Hebrew University, Jerusalem, Israel				X	X	X
Mirna Dzamonja	University of East Anglia, Norwich, UK			X
Marton Elekes	Renyi Institut, Budapest, Hungary				X
Ilijas Farah	York University, Toronto, Canada				X
Barnabas Farkas	Budapest University of Technology and Economics, Hungary			X	X	X	X
Sakae Fuchino	Kobe University, Japan			X
Su Gao	University of North Texas, USA				X	X	X
Mohammad Golshani	IPM, Teheran, Iran			X
Vassilis Gregoriades	Universität Darmstadt, Germany				X
Aaron Hill	University of North Texas, USA				X
Peter Holy	University of Bristol, UK	X	X	X
Daisuke Ikegami	University of California, Berkeley, USA			X
Steve Jackson	University of North Texas, USA				X
Istvan Juhasz	Renyi Institut, Budapest, Hungary			X
Adriane Kaïchouh	Université Lyon 1, France				X
Vladimir Kanovei	Kharkevich Institute, Moscow, Russia				X
Menachem Kojman	Ben Gurion University, Beer-Sheva, Israel			X
Piotr Koszmider	Polish Academy, Warsaw			X
Aleksandra Kwiatkowska	University of California, Los Angeles, USA				X
François Le Maître	ENS de Lyon, France				X
Stephane Leroux	TU Darmstadt, Germany					X
Philipp Lücke	Universität Bonn, Germany			X
Martino Lupini	York University, Toronto, Canada			X	X
Menachem Magidor	The Hebrew University, Jerusalem, Israel	X	X	X	X	X
Maciej Malicki	Polish Academy, Warsaw, Poland				X
Alberto Marcone	University of Udine, Italy				X
Andrew Marks	Caltech, USA				X
Diego Mejia	Kobe University, Japan		X	X	X
Heike Mildenberger	Universität Freiburg, Germany			X
Assaf Rinot	Bar-Ilan University, Israel			X
Christian Rosendal	University of Illinois at Chicago, USA				X	X
Marcin Sabok	Polish Academy, Warsaw, Poland				X
Hiroshi Sakai	Kobe University, Japan			X
Grigor Sargsyan	Rutgers University, USA			X
Ralf Schindler	Universität Münster, Germany	X	X	X
Scott Schneider	University of Michigan, USA				X
David Schrittesser	Universität Münster, Germany	X	X	X	X	X	X
Brandon Seward	University of Michigan, Ann Arbor, USA				X
Dima Sinapova	University of Illinois at Chicago, USA			X
Kostya Slutskyy	University of Copenhagen, Denmark				X
Miodrag Sokic	Caltech, USA				X
Slawomir Solecki	University of Illinois, Urbana-Champaign, USA				X	X
Lajos Soukup	Renyi Institut, Budapest, Hungary			X
Asger Törnquist	University of Copenhagen, Denmark				X	X	X
Todor Tsankov	University of Paris 7, France				X
Robin Tucker-Drob	Caltech, USA				X
Spencer Unger	Carnegie-Mellon University, USA			X
Boban Velickovic	University of Paris 7, France			X
Matteo Viale	University of Torino, Italy			X
Philip Welch	University of Bristol, UK			X
Phillip Wesolek	University of Illinois, Chicago, USA				X
Jay Williams	Caltech, USA				X
Samuel Ziegler	University of Illinois at Chicago, USA				X

Local participants

This lists contains

members of the Kurt Gödel Research Center (KGRC), University of Vienna,
members of the Institute of Discrete Mathematics and Geometry (DMG), Vienna University of Technology,
several international guests to the KGRC.

Name	Affiliation	Week(s)
Name	Affiliation	1	2	3	4	5	6
Carolin Antos-Kuby	KGRC	X	X	X	X	X	X
Vincenzo Dimonte	DMG	X	X	X	X	X	X
Arthur Fischer	KGRC	X	X	X	X	X	X
Vera Fischer	KGRC	X	X	X	X	X	X
Laura Fontanella	KGRC	X	X	X	X	X	X
Sy-David Friedman	KGRC	X	X	X	X	X	X
Micha Gavrilovich	St.Petersburg		X
Martin Grebik	Charles University in Prague, Czech Republic			X
Martin Goldstern	DMG	X	X	X	X	X	X
Stefan Hoffelner	KGRC	X	X	X	X	X	X
Radek Honzik	KGRC	X	X	X	X	X	X
Asaf Karagila	The Hebrew University, Jerusalem, Israel	X	X	X
Ahmad Karimi	Tarbiat Modares University, Tehran, Iran	X	X	X
Jakob Kellner	KGRC	X	X	X	X	X	X
Juliette Kennedy	University of Helsinki, Finland			X
Yurii Khomski	KGRC	X	X	X	X	X	X
Vadim Kulikov	KGRC	X	X	X	X	X	X
Arkady Leiderman	Ben Gurion University, Israel				X
Andrea Medini	KGRC	X	X	X	X	X	X
Diana Carolina Montoya Amaya	KGRC	X	X	X	X	X	X
Victor Selivanov	A.P. Ershov Institute of Informatics Systems, Siberian Branch Russian Academy of Sciences					X	X
Matthias Schröder	KGRC				X	X	X
Anda-Ramona Tanasie	KGRC	X	X	X	X	X	X
Fabio Tonti	KGRC	X	X	X	X	X	X
Victor Torres Perez	KGRC	X	X	X	X	X	X
Boaz Tsaban	Bar-Ilan University, Israel				X	X	X
Jouko Väänänen	University of Helsinki, Finland			X
Jonathan Verner	Charles University in Prague, Czech Republic			X
Zoltán Vidnyánszky	Eötvös Loránd University, Hungary				X	X	X
Wolfgang Wohofsky	DMG	X	X	X	X	X	X
Tin Lok Wong	KGRC	X	X	X	X	X	X
Lyubomyr Zdomskyy	KGRC	X	X	X	X	X	X
Yizheng Zhu	Universität Münster, Germany			X

Program FLC Workshop (week3)

Program FLC Workshop (week 3)

First Day:
    Monday September 23, 2013
Last Day:
    Friday September 27, 2013
Social program:
    Wednesday September 25: Lunch, preceded by a 30-minute walk in the afternoon.

MONDAY September 23
09:00	*— Opening and Registration —*
09:30	David Chodounsky: A report on the Katowice problem.
10:20	— Coffee Break —
11:00	Peter Holy: Locally
. abstract
11:50	— Lunch Break —
14:00	*cancelled* Arthur Apter: The Tall and Measurable Cardinals can Coincide on a Proper Class.
14:30	— Coffee Break —
15:30	Piotr Borodulin-Nadzieja: Geometry of analytic P-ideals. abstract
16:00
16:15	Dima Sinapova: Very good scales, squares, and SCH.
16:45
TUESDAY September 24
09:30	Heike Mildenberger: Finitely Many Near-Coherence Classes of Ultrafilters. abstract
10:20	— Coffee Break —
11:00	Spencer Unger: Aronszajn trees and the successors of a singular cardinal.
11:50	— Lunch Break —
14:00	James Cummings: Forcing and the combinatorics of successors of singulars.
14:30	— Coffee Break —
15:30	Piotr Koszmider: The Banach space
in the Cohen model. abstract
16:00
16:15	Hiroshi Sakai: Separation of
from reflection principles.
16:45
WEDNESDAY September 25
09:30	Ralf Schindler: Does
?. abstract
10:20	— Coffee Break —
11:00	Matteo Viale: Category forcings,
.
11:50
12:30	*— Departure for Social Program (Lunch) from Sensengasse 2a —*
THURSDAY September 26
09:30	Philipp Lücke: Continuous Images of Closed Sets in Generalized Baire Spaces.
10:20	— Coffee Break —
11:00	Assaf Rinot: Hedetniemi's conjecture for uncountable graphs. abstract
11:50	— Lunch Break —
14:00	Mohammad Golshani: Adding a lot of Cohen reals by adding a few..
14:30	— Coffee Break —
15:30	Menachem Kojman: Perfect graph coloring.
16:00
16:15	Grigor Sargsyan: On the strength of the unique branch hypothesis (UBH). abstract
16:45
FRIDAY September 27
09:00	Daisuke Ikegami: Inner models from logics and the generic multiverse. abstract
09:50	— Coffee Break —
10:40	Mirna Dzamonja: Constructions from one Cohen real.
11:10
11:30	Diego Mejia: Rothberger gaps in
ideals. abstract
12:00	— Lunch break —
13:30	No talks scheduled in the afternoon to give time for discussions and collaboration at ESI. Coffee break at 14:30.

Program DST Workshop (week 4)

First Day:
    Monday September 30, 2013
Last Day:
    Friday October 4, 2013
Social program:
    Tuesday October 1, excursion to Rust and dinner.

The following schedule is still preliminary and subject to change.

MONDAY September 30
09:00	*— Opening and Registration —*
09:30	Hiroshi Ando: Ultraproducts, QWEP von Neumann algebras, and the Effros-Marechal topology. abstract
10:20	— Coffee Break —
11:10	Dana Bartošová: Near ultrafilters, groups of automorphisms and unique amenability.
12:00	— Lunch Break
14:00	Kostas Beros: Universal subgroups. abstract
14:50
15:05	Marton Elekes: Ranks on Baire class
functions. abstract
15:35	— Coffee Break —
16:15	Udayan (Dario) Darji: Some examples of universal maps. abstract
16:45
17:00	Miodrag Sokic: Semilattices. abstract
17:30
TUESDAY October 1
09:00	Vassilis Gregoriades: Classes of Polish spaces under effective Borel isomorphism. abstract
09:50	— Coffee Break —
10:20	Aleksandra Kwiatkowska: Projective Fraïssé limits and the pseudo-arc.
11:10
11:25	Samuel Ziegler: Weak equivalence and invariant random subgroups.
11:55	— Lunch Break —
13:30	*— Departure for Social Program (Rust) from Sensengasse 2a —*
WEDNESDAY October 2
09:00	Asger Törnquist: Diagonalizing almost disjoint families.
09:50	— Coffee Break —
10:20	Aaron Hill: Rank-one measure-preserving transformations.
11:10
11:25	Su Gao: A model for rank one transformations. abstract
11:55	— Lunch Break
14:00	Andrew Marks: Borel combinatorics, and countable Borel equivalence relations.
14:50
15:05	Steve Jackson: TBA.
15:35	— Coffee Break —
16:15	Alberto Marcone: The complexity of isometric embeddability between ultrametric Polish spaces with fixed set of distances.
16:45
17:00	Pandelis Dodos: Some recent results in Ramsey Theory. abstract
17:30
THURSDAY October 3
09:00	Robin Tucker-Drob: A von-Neumann algebra free proof of solid ergodicity for Bernoulli shifts.
09:50	— Coffee Break —
10:20	Jay Williams: Cone measures, biembeddability, and isomorphism of Kazhdan groups.
11:10
11:25	Vladimir Kanovei: On the countable cofinality of definable chains in Borel partial orders.
11:55	— Lunch Break
14:00	Christian Rosendal: Large scale geometry of metrisable groups. abstract
14:50
15:05	Maciej Malicki: Non-locally compact Polish groups and essentially countable orbit equivalence relations.
15:35	— Coffee Break —
16:15	Scott Schneider: Simultaneous reducibility of pairs of Borel equivalence relations.
16:45
17:00	Brandon Seward: Locally nilpotent groups and hyperfinite equivalence relations. abstract
17:30
FRIDAY October 4
09:00	Marcin Sabok: Completeness of the isomorphism problem for separable C-algebras*.
09:50	— Coffee Break —
10:20	François Le Maître: Topological generators for full groups. abstract
11:10
11:25	Kostyantyn Slutskyy: Automatic continuity for homomorphisms into free products. abstract
11:55	— Lunch Break
13:45	Todor Tsankov: Weakly almost periodic functions, model-theoretic stability, and minimality of topological groups. abstract
14:35
14:50	Phillip Wesolek: Conjugacy class conditions in totally disconnected locally compact Polish groups.
15:20	— Coffee Break —
16:00	Slawomir Solecki: Dual Ramsey theorem for trees.
16:50
17:05	Tomek Bartoszynski: TBA.
Social events Week 3 On Wednesday Sep 25, 2013, 12:30 participants can come for lunch at Mostalm Gasthof & Meierei Johann Egretzberger, situated in the Vienna Woods. After lunch, there is an optional organized hikig trip. We will reach the Mostalm after a short bus ride followed by a 30-minute walk through the woods. We will meet at 12:30 in front of Zahnklinik, on Sensengasse 2a, 1090 Wien. Week 4 On Tuesday Oct 1, 2013 participants can visit Rust, the "king of wines"-city and then enjoy dinner at the impressive restaurant Mole West, situated above the Neusiedl lake. We will meet at 13:30 in front of Zahnklinik, on Sensengasse 2a, 1090 Wien. Contact ESI For questions regarding accomodation, invitation letters for visa, health insurance etc, please contact the ESI administration via secr@esi.ac.at (and mention that you refer to the Set Theory Programme 2013). Programme Committee For questions regarding the schedule, talks, the social program, and the website, please contact Jakob Kellner via kellner@fsmat.at.

Forcing, Large Cardinals and Descriptive Set Theory

Contents

Sponsors

Venue

Participants

International Participants

Local participants

Program FLC Workshop (week3)

Program FLC Workshop (week 3)

MONDAY September 23

TUESDAY September 24

WEDNESDAY September 25

THURSDAY September 26

FRIDAY September 27

Program DST Workshop (week 4)

MONDAY September 30

TUESDAY October 1

WEDNESDAY October 2

THURSDAY October 3

FRIDAY October 4

Social events

Week 3

Week 4

Contact

ESI

Programme Committee