# SCIENTIFIC PROGRAMS AND ACTIVITIES

May 26, 2018

## Set Theory Seminars

The Fields Institute currently hosts an ongoing Set Theory seminar series, meeting each Friday at 1:30 p.m.

Organizers:
Ilijas Farah,
York University, Juris Steprans, York University

 2002 Thematic Program on Set Theory and Analysis. Seminars held during 2002-03 Seminars held during 2003-04

### Schedule

June 24, 2005
Maxim R. Burke, UPEI
Liftings for category algebras

June 17, 2005
Juris Steprans, York University
A regular CLP-compact space of countable tightness whose square is not CLP-compact

June 10, 2005
Ilijas Farah, York University
Prikry problem for Suslin forcings

June 3, 2005, 1:30-3:00pm
Stevo Todorcevic
Representing Trees as Relatively Compact subsets of the first Baire Class

May 13, 2005, 1:30-3:00 pm, Room 210
Dikran Dikranjan, York University and University of Udine
Characterizing subgroups of the circle and of the compact abelian groups

April 22, 2005, 1:30-3:00 pm, Room 210
Juris Steprans, York University
A pigeon hole type of principle for measure spaces.

April 15, 2005-- 1:30-3:00 pm, Room 210
Goyo Mijares, Universidad Central de Venezuela
Parametrizing the abstract Ellentuck theorem - Part III

April 8, 2005 -- 1:30-3:00 pm, Room 210
Goyo Mijares, Universidad Central de Venezuela
Parametrizing the abstract Ellentuck theorem - Part II

April 1, 2005 -- 1:30-3:00pm, Room 210
Goyo Mijares, Universidad Central de Venezuela
Parametrizing the abstract Ellentuck theorem

March 11, 1:30-3:00pm
Lionel Nguyen Van The, Universite Paris 7
Partitioning Ultrametric Urysohn spaces

SET THEORY MINICONFERENCE
March 4, 2005 -- Room 230
1:30-3:00 p.m. Jean A. Larson, University of Florida
Coloring Paths in the Random Graph

3:30-5:00 p.m. Justin Tatch Moore, Boise State University:
Shelah's conjecture and the L space problem
I will give an overview of two of my recent results:
1. PFA implies that the uncountable linear orders have a five element basis.
2. There is a hereditarily Lindelof, non-separable topological space.
I will give an outline of both proofs and demonstrate that in the case of (1), the new methods which were developed are essential in some quantifiable way; e.g. FA(Axiom A) does not suffice.

5:30-7:00 p.m. Uri Abraham, Carnegie Mellon University and Ben Gurion University
Polychromatic partition relations
A function f from the unordered pairs of \lambda is k-bounded iff there are no k pairs with the same color. A subset X of \lambda is polychromatic iff all pairs from X have different colors. We study the existence of large polychromatic sets for arbitrary 2-bounded colorings. (This is joint work with J. Cummings and C. Smyth.)

February 28, 2005 - Room 210
1:30 - 3:00 p.m. Paul B. Larson, Miami University
Pmax and the nonstationary

February 25, 1:30-3pm
Stuart Zoble, University of Toronto
Proving Projective Determinacy

February 11, 2005
Ilijas Farah, York University
Von Neumann's problem and large cardinals

February 4, 2005
Stevo Todorcevic
Biorthogonal systems and quotient spaces via Baire category methods, Part VI

January 28, 2005
Stevo Todorcevic
Biorthogonal systems and quotient spaces via Baire category methods, Part III

January 21, 2005
Stevo Todorcevic
Biorthogonal systems and quotient spaces via Baire category methods, Part II

January 14, 2005
Stevo Todorcevic
Biorthogonal systems and quotient spaces via Baire category methods

January 7, 2005
Slawek Solecki, University of Illinois, Urbana-Champaign
Local amenability and measure small sets
I will talk about a class of Polish groups which is closely related to a notion of measure small sets (left Haar null sets). The definition of this class of groups is obtained by suitably localizing to the identity element of the notion of amenability. I will present results on the extent of this class. For such groups left Haar null sets have many desired properties (they are a $\sigma$-ideal and have the Steinhaus property). I will give proofs of these results. It turns out that opposite to Polish groups which are amenable at the identity are Polish groups which have a non-Abelian free subgroup at the identity. I will make this precise. For such groups left Haar null sets lose the essential properties they enjoy for amenable at $1$ groups. I will present these results as well.

December 20, 2004
Mike Oliver, University of North Texas
Many quotient Boolean algebras
We develop a technique for constructing large collections of Borel ideals on the natural numbers whose quotient Boolean algebras are pairwise nonismorphic. We apply it to show that there are continuum-many (in fact, at least $E_0$-many) such nonisomorphic Boolean algebras that are quotients by $\tboldsymbol{Pi}^0_3$ ideals.

November 26 - 1:30 p.m.
Ilijas Farah, York University
If you can prove it, then it must be true

November 22 - 1:30 p.m. Library
Taras Banakh, Nipissing University and National University of Lviv
Coherence of semifilters, II
This is a continuation of the previous October's talk. This time we will make emphasis on cardinal characteristics of semifilters (for details, see http://www.franko.lviv.ua/faculty/mechmat/Departments/Topology /booksite.html)
Also we shall discuss a recent joint result with A.Blass asserting that the number of non-coherent ultrafilters is either finite or $\ge c$.

November 12 - 1:30 p.m.
Beatriz Zamora-Aviles, York University
Countable dense homogeneity of definable spaces

November 5 - 1:30 p.m.
Paul Szeptycki, York University
TBA

October 29 - 1:30 p.m.
Taras Banakh, National University of Lviv
Ivan Franko, Nipissing University
Coherence of Semifilters

October 25, 2005 -- 2:30 p.m. Fields Library
Menachem Magidor, Hebrew University
Reflection of Second Order Properties

October 22, 2004 -- 1:30 p.m.
Michael Hrusak, Instituto de Matematicas Unidad Morelia
TBA

October 15, 2004 -- l:30 p.m. Fields Library
Ilijas Farah, York University
TBA

October 8, 2004 -- 1:30 p.m.
Gábor Lukács, Dalhousie University
Structure and cardinal invariants of topological groups

October 1, 2004 -- 1:30 p.m.
Stuart Zoble, University of Toronto
Weak Capturing and Stationary Reflection

September 24, 2004 -- 1:30 p.m.
Stuart Zoble, University of Toronto
Weak Capturing and Stationary Reflection

September 17, 2004 -- 1:30 p.m.
Ilijas Farah, York University
Fubini properties of sigma-ideals

September 1, 2004
Victoria Lubitch, York University
Left-separated spaces and linearly Lindelof spaces

August 25, 2004 -- 1:30 p.m
James Hirschorn, Institut für Formale Logik, University of Vienna
Nonhomogeneous analytic families of trees, part III.

August 18, 2004 --1:30 p.m.
James Hirschorn, Institut für Formale Logik, University of Vienna
Nonhomogeneous analytic families of trees, part II

August 11, 2004 -- 1:30pm
James Hirschorn, Institut für Formale Logik, University of Vienna
Nonhomogeneous analytic families of trees

Aug 4, 2004 --1:30 p.m.
Frank Tall, University of Toronto
Some applications and possible applications of PFA(S)[S]

July 28, 2004 -- 1:30 p.m.
Otmar Spinas
, Christian Albrechts University, Kiel
F_sigma and G_delta splitting families

July 21, 2004 --1:30 p.m.
Stevo Todorcevic
Between the von Neumann and the Control Measure Problems

July 14, 2004 -- p.m.
Piotr Koszmider, Universidade de São Paulo
Banach spaces of continuous functions with few decompositions.

July 7, 2004 -- 1:30 p.m.
Piotr Koszmider, Universidade de São Paulo
On a problem of Rolewicz about Banach spaces that admit support sets.