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2011-12
Fridays
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Speaker and Talk
Title
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Feb. 17, 2012
1:30 - 3 p.m.
Fields Institute,
Room 210 |
NO SEMINAR |
Feb. 24, 2012
1:30 - 3 p.m.
Fields Institute,
Room 210 |
Xianghui Shi
(Beijing Normal University)
A Posner-Robinson 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 Posner-Robinson 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. |
| PAST
SEMINARS 2011-12 |
Feb. 10, 2012
1:30 - 3 p.m.
Fields Institute,
Room 210 |
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.
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Feb. 3, 2012
1:30 - 3 p.m.
Fields Institute,
Room 210 |
Assaf Rinot (Fields
Institute and UTM)
Generalizing Erd?s-Rado 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
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Jan 20
1:30 - 3 p.m.
Fields Institute,
Room 210
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Martino Lupini (York University)
Logic for metric structures and the number of universal
sofic groups
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January 13 2012
1:30 - 3 p.m.
Fields Institute,
Room 210
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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 Borel-measurable 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.
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Dec. 16, 2011
1:30 p.m.
Fields Institute,
Room 210
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Rodrigo R. Dias, (São Paulo)
Indestructibility and selection principles
In this talk we will explore the game-theoretic 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.
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Dec. 2, 2011
1:30 p.m.
Fields Institute,
Room 210
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Peter Burton, (Toronto)
A quotient-like construction concerning elementary submodels,
II
No abstract provided
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Nov.25, 2011
1:30 p.m.
Fields Institute,
Room 210
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Peter Burton, (Toronto)
A quotient-like construction concerning elementary submodels
No abstract provided
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Nov.18, 2011
11:00 a.m.-12:30 pm
Fields Institute,
Room 210
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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.
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Nov.11, 2011
11:00 a.m.-12:30 pm
Fields Institute,
Room 210
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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.
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October 28, 2011
11:00 a.m.-12:30 pm
Fields Institute,
Room 210
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Set Theory and C*-algebras Seminar
Stevo Todorcevic (Toronto)
The unconditional basic sequence problem, revisited
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Wednesday,
October 26 from 11am to 12:30pm
Fields Institute, Stewart Library
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Set Theory and C*-algebras Seminar
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October 21, 2011
1:30pm to 3pm
Fields Institute,
Room 210
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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 pi-character. 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 kappa-complete filters
on regular kappa.)
Set Theory and C* algebras
Friday, October 21 from 11am to 1pm
Fields Institute, third floor
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October 14, 2011
1:30pm to 3pm
Fields Institute,
Room 210
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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
sigma-discrete 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.
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| Friday, October 7 from 11am
to 1pm (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.
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October 7, 2011
1:30pm to 3pm
Fields Institute,
Room 210
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Dilip Raghavan (Kobe)
The Borel almost disjointness number
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September 30, 2011
1:30pm to 3pm
Fields Institute,
Room 210
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Judy Roitman (Kansas)
The Box Problem
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September 16, 2011
1:30pm to 3pm
Fields Institute,
Room 210
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Peter Burton (Toronto)
Productive Lindelofness and a class of spaces considered
by Z. Frolik
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July 22, 2011
1:30pm to 3pm
Fields Institute,
Room 210 |
Assaf Rinot (Toronto)
Recent advances in the theory of strong colorings
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July 15, 2011
1:30pm to 3pm
Fields Institute,
Room 210 |
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.)
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July 8, 2011
1:30p to 3pm
Fields Institute,
Room 210 |
Kostas Tyros (Toronto)
Density Theorems for Trees
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