- Friday, December 7, 1:30-3:00pm in Fields Institue room 210
Vera Fischer (York University
The consistency of $b=\kappa
Abstract: Using finite support iteration of c.c.c. partial orders we
provide a model of $b=\kappa < s=\kappa^+$ for $\kappa$ arbitrary
regular, uncountable cardinal.
- Friday November 30, 1:30-3:00pm in Fields Institute room 210
Greg Hjorth (University of Melbourne, UCLA)
Ends and percolation
Abstract: This is part of joint with Inessa Epstein, where we analyze
countable Borel equivalence relations with many ends and the actions
of groups with many ends. As a consequence of this work we obtain a
result regarding the percolation on non-amenable groups that have
infinite normal amenable subgroups.
- Friday November 23, 1:30-3:00pm in Fields Institute room 210
Marton Elekes (Hungarian Academy of Sciences)
Partitioning multiple covers into many subcovers
abstract
- Friday, November 16th, 1:30-3:00 in Fields room 210
Magdalena Grzech (Politechnika Krakowska)
Complemented subspaces of the Banach space $l_\infty / c_0$
- Friday and Saturday November 9-10.
Conference in honour of the 60th Birthday of Professor Andreas R. Blass
- Friday, November 2, 1:30-3:00pm in Fields Institute room 210
Bernhard Koenig (University of Toronto)
Forcing axioms and two cardinal diamonds, Part 2.
- Friday, October 26, 1:30-3:00pm in Fields Institute room 210
Bernhard Koenig (University of Toronto)
Forcing axioms and two cardinal diamonds
Abstract: I will present some known facts and new results
concerning the consistency of forcing axioms with
two cardinal diamond principles.
- Friday, October 19, 1:30-3:00 in Fields Institute room 210
Arthur Fischer (University of Toronto)
PID in PFA(S)[S].
Abstract: We will demonstrate that the P-ideal dichotomy (PID) holds in
models of the form PFA(S)[S]. Time permitting, we will also discuss how
certain extensions of PID can be shown to hold in such models.
- Friday, October 12, 1:30-3:00 in Fields Institute room 210
Istvan Juhasz (Hungarian Academy of Sciences)
Discrete subspaces of compacta
abstract
- Friday, October 5. NO SEMINAR
- Friday, September 28, 1:30-3:00 in Fields room 210
Asger Tornquist (University of Toronto)
Definable Davies' Theorem, Part II
- Friday, September 21, 1:30-3:00 in Fields room 210
Asger Tornquist (University of Toronto)
Definable Davies' Theorem
Abstract: A result due to Davies states that CH is equivalent to every
real function on the plane being representable as a sum of square
functions, i.e. functions of the form g(x)h(y). We give a definable
version of this theorem: Every real is constructible precisely when every
\Sigma^1_2 function allows a representation as a sum of \Sigma^1_2
squares. We also discuss the possibility of a stronger converse in this
Theorem.
- Friday September 14, 1:30-3:00 in the Fields Institute Room 210
Frank Tall (University of Toronto)
More Topological Applications of PFA(S)[S]
Abstract: We continue our study of the paracompactness of locally compact normal spaces in models of PFA(S)[S]. Using P-ideal dichotomy, we are able to improve our
previous results. The presentation should be understandable to regular seminar
participants, even if they missed my lectures last year on paracompactness.
- Friday, September 7, 1:30-3:00 in Fields Institute Room 210
Logan Hoehn (University of Toronto)
A model theoretic approach in topology
Abstract: The Wallman representation theorem enables one to describe certain properties of compact Hausdorff spaces with sentences in a first order language, which makes them compatible with some model theoretic constructions. We state
this theorem and discuss some of its potential applications and
limitations. As a sample application, we show how a certain result about
colorings of self-maps of compact finite-dimensional metric spaces can be
extended to a broader class of spaces using this approach.
- Friday, June 8, 1:30-3:00pm in Fields Institute Room 210
Frank Tall (University of Toronto)
On the metrizability of hereditarily normal manifolds of dimension > 1.
Abstract: We show that a conjunction of four axioms, three of which are
consequences of PFA and one of which is a consequence of V = L, implies such
manifolds are metrizable. The consistency of such a result is a
long-outstanding conjecture of Peter Nyikos. Two of the axioms are known to
follow from PFA(S)[S]; I conjecture that the other two also follow.
- Friday, June 1, 1:30-3:00pm in Fields Institute Room 210
Paul Szeptycki (York University)
Normality in products with a countable factor.
- Friday May 25. NO SEMINAR
- Friday May 18, 1:30-3:00pm in Fields Institute Room 210
Philip Kremer (Department of Philosophy, University of Toronto)
Dynamic Topological Logic
- Friday May 11, 1:30-3:00 in Fields Institute Room 210
Arthur Fischer (University of Toronto)
'Balogh's Sigma' in models of PFA(S)[S] continued.
- Friday May 4, 1:30-3:00 in Fields Institute Room 210
Arthur Fischer (University of Toronto)
'Balogh's Sigma' in models of PFA(S)[S] continued.
- Friday April 27, 1:30-3:00, Fields Institute, Room 210
Arthur Fischer (University of Toronto)
'Balogh's Sigma' in models of the form PFA(S)[S]
Abstract:
Continuing the study of topological consequences of forcing with the
coherent Souslin tree S in models of PFA(S), we will demonstrate that
the following PFA result also holds: Every locally countable subspace Z
of size À1 in a compact sequential space X is s-closed
discrete in some open neighbourhood of Z in X which "locally
witnesses" the local countability of Z in X.
- Friday April 20, 1:30-3:00, Fields Institute, Room 210
Paul Larson (Miami University, Ohio)
The stationary set splitting game
Abstract: The stationary set splitting game is a game of perfect
information of length w1 between two players, UNSPL and
SPLS, in which UNSPLS chooses stationarily many countable ordinals
and SPLS tries to continuously divide them into two stationary
pieces. We show that it is possible in ZFC to force a winning
strategy for either player, giving a new counterexample to
S22 maximality with a predicate for the nonstationary
ideal on w1. We show that the determinacy of the game is
consistent with Martin's Axiom but not Martin's Maximum. This is joint work
with Saharon Shelah.
- Friday April 13, 1:30-3:00, Fields Institute, room 210
Matthias Neufang (Carleton University)
Decomposition of von Neumann algebras and the Mazur property
Abstract
- Friday April 6. No seminar.
- Friday March 30, 1:30-3:00, Fields Institute, room 210
Wieslaw Kubis (Akademia Swietokrzyska, Poland)
Fraisse sequences and their limis - a category-theoretic approach.
Abstract: Given a category, we define the notion of a Fraisse sequence:
an inductive sequence which shares the
properties of a typical chain of model-theoretic structures producing
the Fraisse-Jonsson limit structure.
We give a criterion for the existence of a Fraisse sequence of a given
length and we shall present some sufficient
conditions for its homogeneity, universality and uniqueness.
For instance: a fixed category may have, up to isomorphism, at most one
countable Fraisse sequence.
We give an example of a certain category of countable trees with many
non-isomorphic Fraisse sequences of
length aleph one.
Finally, we shall present some applications for constructing universal
objects in certain natural categories of
compact spaces, Banach spaces and linearly ordered sets.
- Friday March 23, 1:30-3:00 Fields Institute, room 210
Slawomir Solecki (University of Illinois, USA)
Polish Groups as Isometry Groups.
- Friday March 16, 1:30-3:00 Fields Institute, room 210
Stevo Todorcevic
Chain Conditions in Topology, III (continued)
- Friday March 9, 1:30-3:00 Fields Institute, room 210
Stevo Todorcevic
Chain Conditions in Topology, III
- Friday, February 23, 3:30-5:00 pm Fields Instute Room 230
Andrew Toms
Elliott's program and partially ordered Abelian groups
Abstract: We give a (hopefully) not-too-technical introduction to
Elliott's program to classify separable amenable C*-algebras via K-theoretic
invariants. We will stress the role of partially ordered Abelian groups,
and discuss how the decomposition of such groups into inductive limits of
tractable building blocks gives attractive range results for K-theoretic
invariants. Some time will also be spent on the question of "how many"
such groups may arise as the K-groups of simple C*-algebras. Finally, if
time permits, we will point out some recent results in C*-algebra theory
which have a set theoretic flavour.
- Friday February 9, 1:30-3:00 Fields Institute, room 210
Victoria Lubitch
Note on quasi-Rosenthal compactum.
Abstract: Let X be a Polish space. A compact subset K of R^X is called quasi-Rosenthal if the accumulation points of K are Baire-1 functions. S.A.Argyros, P.Dodos, VKanellopoulos asked whether every quasi-Rosenthal compactum is Frechet. I will present a counter-example.
- Friday February 2, 1:30-3:00 Fields Institute, room 210
Wieslaw Kubis Kielce, Poland
Universal Valdivia compact spaces
Abstract: A space K is Valdivia compact if it is (homeomorphic to) a
closed subset of a Tikhonov cube such that elements with countably many
non-zero coordinates form a dense subset of K.
I will describe the construction of a linearly ordered Valdivia compact
which is a universal increasing pre-image for the class of all linearly
ordered Valdivia compacta. The space has also some homogeneity
properties which, together with universality, characterize it uniquely
up to order isomorphism.
If time permits, I shall also try to sketch the construction of a
universal Valdivia compact for weight $\aleph_1$, under the Continuum
Hypothesis. Again, the space is both universal and in some sense
homogeneous, and these two properties describe it uniquely.
Both constructions can be described as particular cases of a general
theory of Fraisse sequences/limits, in the language of category theory.
- Friday January 26, 1:30-3:00 Fields Institute, Room 210
Luis Pereira Universite Paris VII
Cardinal estimates using a topological approach
Slides from the talk
Abstract: We will prove that Shelah's application of his estimates of the Galvin-Hajnal
norm to cardinal arithmetic can be obtained via Shelah's PCF topology alone.
- Friday January 19, 1:30-3:00 Fields Institute, Room 210
Vladimir Pestov University of Ottawa
Subgroups of metric ultraproducts of unitary and of symmetric
groups: hyperlinear and sofic groups.
Slides from the talk
Abstract: Relatively recently, two new classes of groups have been
isolated: hyperlinear groups and sofic groups. They come from different
corners of mathematics (operator algebras and symbolic dynamics,
respectively), and were introduced independently from each other, but are
closely related nevertheless. Hyperlinear groups are motivated by Connes'
Embedding Conjecture about von Neumann factors of type II_1 and go back to
Connes' work, while sofic groups, introduced by Gromov, are motivated by
Gollschalk surjunctivity conjecture (can a shift A^G contain a proper
isomorphic copy of itself, where A is a finite discrete space and G is a
group?). Groups from both classes can be characterized as subgroups of
metric ultraproducts of families of certain metric groups (formed in the
same way as ultraproducts of Banach spaces): unitary groups of finite rank
lead to hyperlinear groups, symmetric groups of finite rank - to sofic
groups. We will survey results by Connes, Gromov, Benjy Weiss, Ozawa, Elek
and Szabo, Radulescu, and Gordon, and also discuss open questions which
are for the time being perhaps more numerous than the results.
- Friday January 12, 1:30-3:00 Fields Institute, Room 10
Bernhard Koenig, University of Toronto
Coherent trees, continued.
- Friday January 5, 1:30-3:00 Fields Institute, Room 210
Bernhard Koenig, University of Toronto
Coherent trees.
Home
Toronto Set Theory Seminar Year 2006