201112
Fridays


PAST SEMINARS
201112 
June 22 
no seminar 
June 15 
no seminar 
June 8 
Franklin Tall
(Toronto)
Topological Problems for Set Theorists, II
This is the second instalment of a talk I gave 25 years ago,
listing a variety of topological problems with settheoretic
content. The material may be familiar to faculty, but grad
students and postdocs may come across something worth chewing
on.
Posting: http://settheory.mathtalks.org/franklintalltopologicalproblemsforsettheoristsii/
slides available here

June 1 
no seminar 
May 25 
Mike Pawliuk (Toronto)
Set Theoretic attacks on Itzkowitz' problem
In 1976, Gerald Itzkowitz asked if every functionally balanced
group (one where every left uniformly, realvalued function
is right uniformly continuous) is in fact balanced (the left
uniformity and right uniformity coincide). The answer is "Yes"
for topological groups that are even a little bit nice  locally
compact or metrizable or locally connected. The question is
still open in general. I will show how some large topological
groups seem like good candidates for counterexamples. In particular
we will look at isometry groups of large metric spaces like
the Urysohn space.
Posting: http://settheory.mathtalks.org/mikepawliuksettheoreticattacksonitzkowitzproblem/

May 18

Assaf Rinot
(Fields and UTM)
On incompactness for chromatic number of graphs
We shall discuss Shelah's paper #1006. The talk will be an expanded
version of the following blog post. 
May 11

Jim McGarva (Toronto)
Constructing a Taller ThinThick Space

May 4 
no seminar 
April 20 
no seminar 
March 30 
Franklin Tall, University
of Toronto
Lindelof spaces with small pseudocharacter, and an analog
of Borel's Conjecture for subsets of uncountable products of
[0,1]
(With T. Usuba) We improve results of Shelah, myself, and Scheepers
concerning the cardinality of Lindelof spaces with small pseudocharacter.
We establish the consistency, modulo an inaccessible, of an
equivalent of Borel's Conjecture "stepped up one cardinal".

March 23

Miodrag Sokic, Caltech
The Ramsey property for structures with an arbitrary linear
ordering
The class of finite ultrametric spaces with an arbitrary linear
ordering is not a Ramsey class. Also the class of finite posets
with an arbitrary linear ordering is not a Ramsey class. We
will calculate the Ramsey degrees for these classes.

March 16 
Dimitrios Vlitas
(Paris)
An infinite self dual theorem
Recall that the classical Ramsey theorem states that given
any finite coloring of the set of all K elements subsets of
? there exists of an infnite subset A ? ? where the restriction
of the coloring is constant.
The dual form of Ramsey theorem, the CarlsonSimpson Theorem,
states that given any finite Borel coloring of the set of
all partitions of ? into K many classes, there exists a partition
r of ? into ? many classes such that the set of all K partitions
of ? resulting by identifying classes of r is monochromatic.
There are also the corresponding ?nite versions of these
results, the finite Ramsey Theorem, and the GrahamRothschild
theorem, respectively. S. Solecki recently proved a self dual
theorem that implies simultaneously the finite version of
the Ramsey theorem and the GrahamRothschild theorem. He achieved
that by introducing the notion of a connection, which roughly
speaking is a labelled partition of L into K many classes,
for K and L integers. He then proved that given any positive
integers K, L and M there exists N such that for any L coloring
of all labelled partitions of N into K many pieces, there
exists a labelled partition of M into K pieces, such that
the set of all labelled partitions of N into M composed with
the particular labelled partition of M into K is monochromatic.
The composition is defined in the most natural way by composing
partitions, namely that partition N into M pieces and then
M into K pieces, so we finally partition N into K. The
composition of the label functions is done in the reverse
order.
We extend canonically his notion of connection to labeled
partitions of ?, with finite or infinitely many classes and
we prove the following:
Theorem. For any fnite Borel coloring of al l label
led Kpartitions of ? there is a fixed label led ?partition
of ? such that the set of al l of its reductions, i.e. label
led Kpartitions of ? which result from putting pieces of
the ?xed partition together, is monochromatic.
The proof is done by induction on K and the use of the left
variable HalesJewett Theorem. In the ?nal section of the
paper we extend this result by building the corresponding
topological Ramsey space F?,? .

March 9

Paul McKenney
(CMU)
Automorphisms of Calkin Algebras 
March 2 
Santi Spadaro
(York)
Noetherian type and other topological cardinal invariants
of an ordertheoretic flavour
Noetherian type is a cardinal function that was introduced
by Peregudov in the 90s to capture some base properties studied
by the Russian School in the 70s. It has a striking affinity
to the Suslin Number and for this reason it has an interesting
productive behavior. We will show an example of two spaces
of uncountable Noetherian type whose product has countable
Noetherian type and single out classes of spaces in which
the Noetherian type cannot decrease by passing from a space
to its square. Time permitting we will show some independence
results regarding the Noetherian type of countably supported
box products. This is joint work with Menachem Kojman and
Dave Milovich.

Feb. 24 
Xianghui Shi
(Beijing Normal University)
A PosnerRobinson Theorem from Axiom I_0
Under a slightly stronger version of Axiom I_0: there is
a *proper* elementary embedding j from L(V_{lambda+1}) to L(V_{lambda+1})
with critical point < lambda, we prove an analog of Perfect
Set Theorem in the context of V_{lambda+1}. And as a collorary,
we obtain a version of PosnerRobinson Theorem at V_{lambda+1}:
for every A in V_{\lambda+1}, and for almost every B in V_{\lambda+1}
(i.e. except a set of size lambda) that can compute A, there
is a G in V_{lambda+1}$ such that G joint B can compute the
sharp of G. Here ``compute'' and ``joint'' are analogs of the
notions in the structure of Turing degrees. This is a part of
the study on the impact of large cardinal hypotheses on various
generalized degree structures. 
Feb. 17 
NO SEMINAR 
Feb. 10 
Slawomir Solecki
(UIUC)
An abstract approach to Ramsey theory with applications to finite
trees
I will present an abstract approach to finite Ramsey theory.
I will indicate how certain concrete Ramsey results for finite
trees are obtained by applying the abstract result.

Feb. 3 
Assaf Rinot (Fields
Institute and UTM)
Generalizing Erd?sRado to singular cardinals
One of the most famous implications of the infinite Ramsey theorem
(1929) asserts that any infinite poset either contains an infinite
antichain or an infinite chain. Ramsey's theorem has been generalized
by Dushnik and Milner (1941), and subsequently by Erd?s to a
theorem that implies that any poset of uncountable cardinality
k either contains an antichain of size k, or an infinite chain.
Is it possible to ask for a more sophisticated second alternative?
More specifically, can the theorem be strengthened to yield
the existence of an infinite chain *with a maximal element*?
This question, restricted to uncountable regular cardinals,
was answered by Erdos and Rado (1956).
In this talk, we shall discuss the missing case  singular
cardinals  and present a proof of a Theorem of Shelah (2009)
in the positive direction. Our proof may be found in here:
http://blog.assafrinot.com/?p=628

Jan. 20

Martino Lupini (York University)
Logic for metric structures and the number of universal
sofic groups

Jan.13

Jan Pachl, (Fields)
Measurable centres in convolution semigroups
Every topological group G naturally embeds in larger spaces,
algebraically and topologically. Two such convolution semigroups
of particular interest in abstract harmonic analysis are the
norm dual of the space of bounded right uniformly continuous
functions on G, and the uniform compactification of G with
its right uniformity. Our understanding of the structure of
these spaces has been advanced by tractable characterizations
of their topological centres, now available for "almost
all" topological groups. In the seminar I will discuss
a measurable analogue of the topological centre, for various
notions of measurability. This notion was investigated by
Glasner (2009) for the compactification of a discrete group,
using Borel measurability.
The main result is that in convolution semigroups over locally
compact groups the Borelmeasurable centre coincides with
the topological centre [arXiv:1107.3799]. It is an open question
whether the same holds for all topological groups. One version
of the similar statement in which universal measurability
replaces Borel measurability is independent of ZFC.

Dec. 16

Rodrigo R. Dias, (São Paulo)
Indestructibility and selection principles
In this talk we will explore the gametheoretic characterization
of indestructibility of Lindelöf spaces. In particular,
we will show that this property is not equivalent to the associated
selection principle if CH is assumed.

Dec. 2

Peter Burton, (Toronto)
A quotientlike construction concerning elementary submodels,
II
No abstract provided

Nov.25

Peter Burton, (Toronto)
A quotientlike construction concerning elementary submodels
No abstract provided

Nov.18

Konstantinos Tyros (Toronto)
Density theorems for strong subtrees
In this talk we will present the main ingredients of the proof
of the density version of Halpern Lauchli Theorem. We shall
also discuss some of its applications.

Nov.11

Natasha May (York)
A Noetherian base for scattered linear orders
A collection of sets is Noetherian if it contains no infinite
ascending sequences. We show that every scattered LOTS of
cardinality strictly less than the first strongly inaccessible
cardinal has a Noetherian base. I will also provide
some motivation. Joint with Paul Szeptycki.

Oct. 28

Set Theory and C*algebras Seminar
Stevo Todorcevic (Toronto)
The unconditional basic sequence problem, revisited

Oct. 26
11:00 am

Set Theory and C*algebras Seminar

Oct. 21

David Milovich (Texas A&M International)
On cofinal types in compacta: cubes, squares, and forbidden
rectangles
In every compactum, not every point's neighborhood filter
has cofinal type omega times omega_2. (This is an instance
of a more general theorem.) This can be interpreted as
yet another partial result pointing toward the conjectures that
homogeneous compacta cannot have cellularity greater than
c (Van Douwen's Problem) nor an exponential gap between character
and picharacter. There are compacta where every point's neighborhood
filter has cofinal type omega times omega_1, but it is
not known if there is a homogeneous compactum with this
property.
Continuing the theme of cofinal types of product orders, the Fubini
cube and Fubini square of an arbitrary filter F on omega are
cofinally equivalent to each other and to the direct product
F^omega. (This generalizes to kappacomplete filters
on regular kappa.)

Friday, October
21
11:00 a.m.
Stewart Library 
Set Theory and C*
algebras

Oct. 14

Daniel Soukup (Toronto)
Variations on separability
The aim of this talk is to review some recent results
on variations of separability; we investigate spaces having
sigmadiscrete and meager dense sets and selective versions
of these properties. Our results mostly determine the relations
between these properties, as well as give some hint on the
effect of various convergence properties on these weak types
of separability. However, many questions are left open. This
work was jointly done by D. Soukup, L. Soukup and S. Spadaro.

Oct. 7
11:00 a.m.
Room 210 
A special seminar on Set
Theory and C*algebras.
The first goal is to read the paper "Turbulence, orbit
equivalene, and the classification of C*algebras" by Farah/Toms/Törnquist.

Oct. 7

Dilip Raghavan (Kobe)
The Borel almost disjointness number

Sept.30

Judy Roitman (Kansas)
The Box Problem

Sept. 16

Peter Burton (Toronto)
Productive Lindelofness and a class of spaces considered
by Z. Frolik

July 22

Assaf Rinot (Toronto)
Recent advances in the theory of strong colorings

July 15 
Franklin Tall (Toronto)
Recent progress and problems concerning Lindelöf products
and selection principles.
Rodrigo Dias (Toronto)
Some topological games and selection principles
(Please note that Franklin Tall will also give two talks,
on July 12 and 19 in Bahen 6180/3 at 11am in the student set
theory seminar. The titles are PFA(S)[S]: topological applications
of forcing with coherent Souslin trees, AND PFA(S)[S]: a method
for proving a set of size aleph_1 is the union of countable
many nice subsets.)

July 8, 2011

Kostas Tyros
(Toronto)
Density Theorems for Trees 