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).

    S. D. Friedman (U. Wien), M. Goldstern (TU Wien), A. Kechris (Caltech, USA), J. Kellner (U. Wien), W. H. Woodin (UC Berkeley, USA)
    September 9 - October 18, 2013
    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.


The principal contributor is the ESI.

We gratefully acknowledge additional support from the following sources:


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).


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

Hiroshi AndoIHES, FranceX
Alessandro AndrettaUniversity of Torino, ItalyX
Giorgio AudritoUniversity of Torino, ItalyX
Joan BagariaUniversity of Barcelona, SpainX
Dana BartosovaUniversity of Toronto, CanadaX
Tomek BartoszynskiNational Science Foundation, USAXX
Kostas BerosUniversity of Wisconsin, USAX
Piotr Borodulin-NadziejaUniversity of Wroclaw, PolandX
Riccardo CamerloPolitecnico di Torino, ItalyX
David ChodounskyAcademy of Sciences of the Czech RepublicX
James CummingsCarnegie-Mellon University, USAXX
Udayan DarjiUniversity of Louisville, Kentucky, USAX
Gabriel DebsUniversity of Le Havre and Institut Mathematique de Jussieu, FranceX
Pandelis DodosUniversity of Athens, GreeceX
Gregor DolinarUniversity of Ljubljana, SloveniaX
Ohad DruckerThe Hebrew University, Jerusalem, IsraelXXX
Mirna DzamonjaUniversity of East Anglia, Norwich, UKX
Marton ElekesRenyi Institut, Budapest, HungaryX
Ilijas FarahYork University, Toronto, CanadaX
Barnabas FarkasBudapest University of Technology and Economics, HungaryXXXX
Sakae FuchinoKobe University, JapanX
Su GaoUniversity of North Texas, USAXXX
Mohammad GolshaniIPM, Teheran, IranX
Vassilis GregoriadesUniversität Darmstadt, GermanyX
Aaron HillUniversity of North Texas, USAX
Peter HolyUniversity of Bristol, UKXXX
Daisuke IkegamiUniversity of California, Berkeley, USAX
Steve JacksonUniversity of North Texas, USAX
Istvan JuhaszRenyi Institut, Budapest, HungaryX
Adriane KaïchouhUniversité Lyon 1, FranceX
Vladimir KanoveiKharkevich Institute, Moscow, RussiaX
Menachem KojmanBen Gurion University, Beer-Sheva, IsraelX
Piotr KoszmiderPolish Academy, WarsawX
Aleksandra KwiatkowskaUniversity of California, Los Angeles, USAX
François Le MaîtreENS de Lyon, FranceX
Stephane LerouxTU Darmstadt, GermanyX
Philipp LückeUniversität Bonn, GermanyX
Martino LupiniYork University, Toronto, CanadaXX
Menachem MagidorThe Hebrew University, Jerusalem, IsraelXXXXX
Maciej MalickiPolish Academy, Warsaw, PolandX
Alberto MarconeUniversity of Udine, ItalyX
Andrew MarksCaltech, USAX
Diego MejiaKobe University, JapanXXX
Heike MildenbergerUniversität Freiburg, GermanyX
Assaf RinotBar-Ilan University, IsraelX
Christian RosendalUniversity of Illinois at Chicago, USAXX
Marcin SabokPolish Academy, Warsaw, PolandX
Hiroshi SakaiKobe University, JapanX
Grigor SargsyanRutgers University, USAX
Ralf SchindlerUniversität Münster, GermanyXXX
Scott SchneiderUniversity of Michigan, USAX
David SchrittesserUniversität Münster, GermanyXXXXXX
Brandon SewardUniversity of Michigan, Ann Arbor, USAX
Dima SinapovaUniversity of Illinois at Chicago, USAX
Kostya SlutskyyUniversity of Copenhagen, DenmarkX
Miodrag SokicCaltech, USAX
Slawomir SoleckiUniversity of Illinois, Urbana-Champaign, USAXX
Lajos SoukupRenyi Institut, Budapest, HungaryX
Asger TörnquistUniversity of Copenhagen, DenmarkXXX
Todor TsankovUniversity of Paris 7, FranceX
Robin Tucker-DrobCaltech, USAX
Spencer UngerCarnegie-Mellon University, USAX
Boban VelickovicUniversity of Paris 7, FranceX
Matteo VialeUniversity of Torino, ItalyX
Philip WelchUniversity of Bristol, UKX
Phillip WesolekUniversity of Illinois, Chicago, USAX
Jay WilliamsCaltech, USAX
Samuel ZieglerUniversity of Illinois at Chicago, USAX

Local participants

This lists contains

Carolin Antos-KubyKGRCXXXXXX
Vincenzo DimonteDMGXXXXXX
Arthur FischerKGRCXXXXXX
Laura FontanellaKGRCXXXXXX
Sy-David FriedmanKGRCXXXXXX
Micha GavrilovichSt.PetersburgX
Martin GrebikCharles University in Prague, Czech RepublicX
Martin GoldsternDMGXXXXXX
Stefan HoffelnerKGRCXXXXXX
Asaf KaragilaThe Hebrew University, Jerusalem, IsraelXXX
Ahmad KarimiTarbiat Modares University, Tehran, IranXXX
Juliette KennedyUniversity of Helsinki, FinlandX
Arkady LeidermanBen Gurion University, IsraelX
Diana Carolina Montoya AmayaKGRCXXXXXX
Victor SelivanovA.P. Ershov Institute of Informatics Systems, Siberian Branch Russian Academy of SciencesXX
Matthias SchröderKGRCXXX
Anda-Ramona TanasieKGRCXXXXXX
Victor Torres PerezKGRCXXXXXX
Boaz TsabanBar-Ilan University, IsraelXXX
Jouko VäänänenUniversity of Helsinki, FinlandX
Jonathan VernerCharles University in Prague, Czech RepublicX
Zoltán VidnyánszkyEötvös Loránd University, HungaryXXX
Wolfgang WohofskyDMGXXXXXX
Lyubomyr ZdomskyyKGRCXXXXXX
Yizheng ZhuUniversität Münster, GermanyX

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 —
09:30David Chodounsky:
   A report on the Katowice problem.
10:20— Coffee Break —
11:00Peter Holy:
. abstract
11:50— Lunch Break —
Arthur Apter: The Tall and Measurable Cardinals can Coincide on a Proper Class.
14:30— Coffee Break —
15:30Piotr Borodulin-Nadzieja:
   Geometry of analytic P-ideals. abstract
16:15Dima Sinapova:
   Very good scales, squares, and SCH.

TUESDAY September 24

09:30Heike Mildenberger:
   Finitely Many Near-Coherence Classes of Ultrafilters. abstract
10:20— Coffee Break —
11:00Spencer Unger:
   Aronszajn trees and the successors of a singular cardinal.
11:50— Lunch Break —
14:00James Cummings:
   Forcing and the combinatorics of successors of singulars.
14:30— Coffee Break —
15:30Piotr Koszmider:
   The Banach space
in the Cohen model. abstract
16:15Hiroshi Sakai:
   Separation of
from reflection principles.

WEDNESDAY September 25

09:30Ralf Schindler:
?. abstract
10:20— Coffee Break —
11:00Matteo Viale:
   Category forcings,
12:30— Departure for Social Program (Lunch) from Sensengasse 2a —

THURSDAY September 26

09:30Philipp Lücke:
   Continuous Images of Closed Sets in Generalized Baire Spaces.
10:20— Coffee Break —
11:00Assaf Rinot:
   Hedetniemi's conjecture for uncountable graphs. abstract
11:50— Lunch Break —
14:00Mohammad Golshani:
   Adding a lot of Cohen reals by adding a few..
14:30— Coffee Break —
15:30Menachem Kojman:
   Perfect graph coloring.
16:15Grigor Sargsyan:
   On the strength of the unique branch hypothesis (UBH). abstract

FRIDAY September 27

09:00Daisuke Ikegami:
   Inner models from logics and the generic multiverse. abstract
09:50— Coffee Break —
10:40Mirna Dzamonja:
   Constructions from one Cohen real.
11:30Diego Mejia:
   Rothberger gaps in
ideals. abstract
12:00— Lunch break —
13:30No 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 —
09:30Hiroshi Ando:
   Ultraproducts, QWEP von Neumann algebras, and the Effros-Marechal topology. abstract
10:20— Coffee Break —
11:10Dana Bartošová:
   Near ultrafilters, groups of automorphisms and unique amenability.
12:00— Lunch Break
14:00Kostas Beros:
   Universal subgroups. abstract
15:05Marton Elekes:
   Ranks on Baire class
functions. abstract
15:35— Coffee Break —
16:15Udayan (Dario) Darji:
   Some examples of universal maps. abstract
17:00Miodrag Sokic:
   Semilattices. abstract

TUESDAY October 1

09:00Vassilis Gregoriades:
   Classes of Polish spaces under effective Borel isomorphism. abstract
09:50— Coffee Break —
10:20Aleksandra Kwiatkowska:
   Projective Fraïssé limits and the pseudo-arc.
11:25Samuel Ziegler:
   Weak equivalence and invariant random subgroups.
11:55— Lunch Break —
13:30— Departure for Social Program (Rust) from Sensengasse 2a —


09:00Asger Törnquist:
   Diagonalizing almost disjoint families.
09:50— Coffee Break —
10:20Aaron Hill:
   Rank-one measure-preserving transformations.
11:25Su Gao:
   A model for rank one transformations. abstract
11:55— Lunch Break
14:00Andrew Marks:
   Borel combinatorics, and countable Borel equivalence relations.
15:05Steve Jackson:
15:35— Coffee Break —
16:15Alberto Marcone:
   The complexity of isometric embeddability between ultrametric Polish spaces with fixed set of distances.
17:00Pandelis Dodos:
   Some recent results in Ramsey Theory. abstract

THURSDAY October 3

09:00Robin Tucker-Drob:
   A von-Neumann algebra free proof of solid ergodicity for Bernoulli shifts.
09:50— Coffee Break —
10:20Jay Williams:
   Cone measures, biembeddability, and isomorphism of Kazhdan groups.
11:25Vladimir Kanovei:
   On the countable cofinality of definable chains in Borel partial orders.
11:55— Lunch Break
14:00Christian Rosendal:
   Large scale geometry of metrisable groups. abstract
15:05Maciej Malicki:
   Non-locally compact Polish groups and essentially countable orbit equivalence relations.
15:35— Coffee Break —
16:15Scott Schneider:
   Simultaneous reducibility of pairs of Borel equivalence relations.
17:00Brandon Seward:
   Locally nilpotent groups and hyperfinite equivalence relations. abstract

FRIDAY October 4

09:00Marcin Sabok:
   Completeness of the isomorphism problem for separable C*-algebras.
09:50— Coffee Break —
10:20François Le Maître:
   Topological generators for full groups. abstract
11:25Kostyantyn Slutskyy:
   Automatic continuity for homomorphisms into free products. abstract
11:55— Lunch Break
13:45Todor Tsankov:
   Weakly almost periodic functions, model-theoretic stability, and minimality of topological groups. abstract
14:50Phillip Wesolek:
   Conjugacy class conditions in totally disconnected locally compact Polish groups.
15:20— Coffee Break —
16:00Slawomir Solecki:
   Dual Ramsey theorem for trees.
17:05Tomek Bartoszynski:

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.



For questions regarding accomodation, invitation letters for visa, health insurance etc, please contact the ESI administration via (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