200910

PAST SEMINARS 
Friday, June 25,
1:303:00 (location to be announced).

Adam Ostaszewski (London School of Economics
and Political Science)
Title: TBA

June 19,
1:303:00
Room 230 
Ilijas Farah (York University)
All automorphisms of all Calkin algebra (continued)
(Joint work with Paul McKenney and Ernest Schimmerling)
I will prove that PFA implies that all automorphisms of the
Calkin algebra associated with any infinitedimensional Hilbert
space are inner.

June 11, 2010 
Ilijas Farah (York University)
TBA 
June 4, 2010 
Dilip Raghavan (University
of Toronto)
Distinguishing two cardinal invariants of the continuum

May 28, 2010

*** SEMINAR CANCELED *** 
May 14, 2010

*** SEMINAR CANCELED *** 
May 7, 2010
10:30 a.m.
Room 230

Franklin D Tall (University
of Toronto)
Productively Lindelof spaces may all be D
I will prove that the Continuum Hypothesis implies every
productively Lindelof space is a Dspace. Collateral damage
includes that Borel's Conjecture implies every Rothberger
space is Hurewicz.

May 7, 2010
1:30 p.m.
Room 210 
Brice Minaud (Paris)
Reflection principle implies the singular cardinal hypothesis,
a simplified version of a proof by Shelah cont.
Shelah proved in 2004 that Stationary Set Reflection implies
SCH. We present a simpler version of the proof, involving a
closed game. 
April 30, 2010 
Teruyuki Yorioka (Shizuoka
University)
Aronszajn trees and weak fragments of Martin's Axiom
I will talk a summary of the following papers:
(1) Some Weak fragments of Martin's Axiom related to the rectangle
refining property , Arch. Math. Logic 47 (2008), 7990.
(2) The inequality $\mathfrak{b}>\aleph_1$ can be considered
as an analogue of Suslin's Hypothesis , Axiomatic Set Theory
and Settheoretic Topology (Kyoto 2007), S?rikaisekikenky?sho
K?ky?roku No. 1595 (2008), 8488.
(3) A nonimplication between fragments of Martin's Axiom related
to some property which comes from Aronszajn trees , Ann. Pure
Appl.Logic, 161 (2010), 469487.
(4) Uniformizing Ladder system colorings and the rectangle refining
property , Proc. Amer. Math. Soc., to appear. (For (1), (2),
(3), see Shizuoka University repository which is linked from
my webpage: http://www.ipc.shizuoka.ac.jp/~styorio/ For (4),
see Recently posted articles in PAMS website.)
In these papers, some combinatorial properties of forcing notions
are introduced. All of them originate from an analysis of Aronszajn
trees, and are stronger than the countable chain condition.
We argue some consistency results about fragments of MA_{aleph_1}
restricted to forcing notions with their properties. In the
talk, we prove that forcing notions with such properties add
no random reals.

April 23, 2010 
Brice Minaud (Paris)
Reflection principle implies the singular cardinal hypothesis,
a simplified version of a proof by Shelah
Shelah proved in 2004 that Stationary Set Reflection implies
SCH. We present a simpler version of the proof, involving
a closed game.

April 16, 2010 
Leandro Aurichi (Sao Paolo)
Strongly Dspaces
We will talk about a condition that is stronger than being D
and that implies Lindelofness.

April 9, 2010 
Ralf Schindler (Universität
Münster)
Bounded forcing axioms and Pi2 statements
Many natural Pi2 consequences of Martin's Maximum have been
verified to follow from Bounded Martin's Maximum plus the statement
that NS, the nonstationary ideal on \omega_1, be precipitous.
The forcing whose variants are exploited here is semiproper
if and only if all stationary set preserving forcings are semiproper.

March 26, 2010 
Carlos Azarel (University
of Toronto)
Gap Structure of Coherent Aronszajn Trees (continued)
We give a detailed description of the gap structure of $({\cal
C},\prec)$ (the class of coherent Aronszajn trees) under the
assumption of $MA_{\omega_1}$. Our study on gaps shows that
the class $ MA_{\omega_1}$ is universal for all linear orders
of cardinality at most $\aleph_2$, i.e.$({\cal C},\prec)$ contains
an isomorphic copy of each linear ordered set of size less or
equal than $\aleph_2$.

March 19, 2010 
Carlos Azarel (University
of Toronto)
Gap Structure of Coherent Aronszajn Trees
We give a detailed description of the gap structure of $({\cal
C},\prec)$ (the class of coherent Aronszajn trees) under the
assumption of $MA_{\omega_1}$. Our study on gaps shows that
the class $MA_{\omega_1}$ is universal for all linear orders
of cardinality at most $\aleph_2$, i.e. $({\cal C},\prec)$ contains
an isomorphic copy of each linear ordered set of size less or
equal than $\aleph_2$.

March 12, 2010 
Benjamin Miller
Defining nonempty small sets from families of infinite
sets
We consider circumstances under which nonempty small subsets
of a space can be defined from families of infinite subsets
of the space, in the process establishing generalizations of
Mansfield's perfect set theorem and the LusinNovikov uniformization
theorem.

***Special Day
and Time***
March 10, 2010
3:30 p.m.
Stewart Library

Ryszard Frankiewicz (IM PAN,
Warsaw)
Remarks on covering by nowhere Ramsey sets

March 5, 2010 
Frank Tall (University of Toronto)
Productively Lindelof Spaces
A space is productively Lindelof if its product with every Lindelof
space is Lindelof. We have a variety of new results about such
spaces, obtained via assorted settheoretic methods.

February 19, 2010 

February 12, 2010 
David Milovich (Texas A&M
International)
On the order theory of local bases
The local Noetherian type of a point in a space is the least
kappa such that that point has a local base that is kappalike
with respect to the containment ordering.Local Noetherian type
is surprisingly connected to Van Douwen's Problem. GCH implies
that the local Noetherian type of point in a homogeneous compactum
cannot exceed the cellularity of that space. All known homogeneous
compacta have cellularity at most $2^{\aleph_0}$ and local Noetherian
type at most $\aleph_0$. Local Noetherian type is even more
closely connected to Tukey reducibility. Indeed, it is at the
heart of Isbell's Problem, which can be formulated as asking
whether the StoneCech remainder of omega has a point with uncountable
local Noetherian type (assuming only ZFC). For a connection
to large cardinals, consider the local Noetherian type of an
arbitrary point in the $G_\delta$ modification of $2^{\aleph_\omega}$.
It is $\aleph_1$ assuming V=L; it is $\aleph_2$ assuming GCH
and Chang's Conjecture at $\aleph_\omega$. My talk will (1)
survey basic facts about local Noetherian types and connections
mentioned above, (2) survey recent results about limit cardinals
and product topologies, and (3) mention some results from the
more difficult theories of (global) Noetherian type and Noetherian
$\pi$type. 
January 22

NO SEMINAR

February 5

NO SEMINAR

January 22

NO SEMINAR

January 15
1:303:00
Stewart Library

Frank Tall
(University of Toronto)
Settheoretic problems concerning Lindelof spaces
We survey a variety of classic problems involving Lindelof spaces
that have partial settheoretic solutions. These are good research
problems for graduate students in set theory or settheoretic
topology.

January 8

Talk Cancelled

Dec. 18
1:303:00
Room 210 
Márton Elekes (University
of Toronto)
Haar null sets and the consistent reflection of nonmeagerness
in Cantor sets 
Dec. 11
1:303:00
Room 210

Ilijas Farah (York University)
A dichotomy for the number of ultrapowers (continued).
(joint work with S. Shelah.) The paper is now available at:
http://www.math.yorku.ca/~ifarah/preprints.html

Dec. 4, 1:30pm
Room 210

Logan Hoehn (University of Toronto)
A counterexample for Lelek's problem in continuum theory

Nov. 27, 1:30pm
Room 210

Ilijas Farah (York University)
A dichotomy for the number of ultrapowers
(joint work with S. Shelah.)

Nov. 20, 1:30pm
Room 210

David Fremlin (University of Essex)
TBA

Nov. 13, 1:30pm
Room 210

No talk scheduled

Nov. 6, 1:30pm
Room 210

Miodrag Sokic (University of Toronto)
Ramsey properties of finite posets, continued

October 30 at 1:30pm
Room 210 
no talk scheduled 
October 23 at 1:30pm
Room 210

David Fremlin (University of Essex)
Various kinds of ultrafilter
content: extracts from
http://www.essex.ac.uk/maths/staff/fremlin/n09102.ps

October 16 at 3:30pm
Room 210 
Frank Tall (University of Toronto)
Applying PFA(S)[S]  some of the tools
One of the aspects of Todorcevic's proof that PFA(S)[S] implies
that "in compact countably tight spaces, locally countable
subsets of size aleph_1 are sigmadiscrete" is a general
method for forcing certain collections to be 'sigmasmall'.
We will talk about this method, and work in progress applying
it to problems concerning under what circumstances does normality
imply collectionwise Hausdorffness.

October 16 at 1:30pm
Room 210

Miodrag Sokic (University of Toronto)
Ramsey properties of finite posets
Using result of KechirsPestovTodor?evi? we analyise Fraïssé
classes of finite posets. In order to conduct such analysis
we have to examine various classes of finite posets with linear
orderings. There are two natural ways we can add linear orderings:
to be arbitrary or to be linear extension of partial orderings.
Our discussion contains examinantion of ordering property
and Ramsey property of such classes where we use techinque
of partite construction and concept of acolored sets. On
the end we give topological meaning of the previous obtained
combinatorila results and give list of few extremely amenable
groups as well as list of few universal minimal flows.

October 9 at 1:30pm
Room 210

Dilip Raghavan (University of Toronto)
A model with no strongly completely separable MAD families,
continued

October 2 at 1:30pm
Room 210

Boris Model (Ben Gurion University in the Negev)
On the Theory of Infinite Stage Games of Search and Completion
On the border of Games Theory and Set Theory there is a broad
class of Infinite Stage Decision Making Processes that can
be characterized by the main followingproperty: a Future development
of the process depends on the process Present state and does
not depend directly on the process Past [1]. As an example
of such kind ofprocesses and some connected with them questions
Infinite Stage Games of Search and Completion [2, 3], which
are interesting by themselves also, are presented. For these
games (of the same nature as for example chess and draughts
have: a Future depends on the Present and does not depend
directly on the Past) with the use ofcontinuum hypothesis
much unexpected results can be proved, for example: The least
guaranteed result of these simultaneously played but completely
independent gamesturns out to be less than the sum of the
least guaranteed results of constituent games (and not equal
to this sum as it could be supposed and as it is in the case
of chess or draughts!).
References
1. B. I. Model’, The existences of an overall ?optimal
strategy and
validity of Bellman’sfunctional equation in an extended
class of dynamic processes. I; II, Engineering Cybernetics,
No. 5, 1975, pp. 13 – 19; No. 6, 1975, pp. 12 –
19.
2. B. I. Model’, Games of search and completion, Journal
of Mathematical Sciences, Vol. 80, No 2,
1996, pp. 1699  1744, Plenum Publishing Corporation, New
York.
3. U. Abraham, R. Schipperus, Infinite Games on Finite Sets,
Israel Journal of Mathematics, Vol. 159, 2007, pp. 205 219.


Gregory Chaitin (IBM Thomas J. Watson Research Centre)
Leibniz, Complexity & Incompleteness

September 18 at 1:30pm
Room 210 
Dilip Raghavan (University of Toronto)
A model with no strongly completely separable MAD families

August 28 at 1:30pm
Room 210 
Maxime Burke (University of Prince Edward Island)
Approximating smooth functions by "generic" entire
functions

August 21 at 1:30pm
Room 210 
Dilip Raghavan (University of Toronto)
Cofinal Types of Ultrafilters

August 14 at 1:30pm
Room 210 
Asger Tornquist (University of Vienna)
On the pointwise implementation of measure preserving actions,
continued

August 7 at 1:30pm
Room 210 
Asger Tornquist (University of Vienna)
On the pointwise implementation of measure preserving actions

Tuesday, July 14, at 3:30pm5:00pm in BA2195,

Of interest:
Sean Saunders will give a presentation for his Master's
summer project:
Van der Waerden's Theorem and Hindman's Theorem: Topological
Dynamics Proofs of Theorems in Number Theory. 