Set Theory Seminar, Fall
2009
Our seminars are on Tuesdays in the Math/Geo building, room 120, 2:40 - 3:30, unless otherwise indicated.
November 10
October 8 - November 3
October 2
Liljana Babinkostova
Generalizations of covering dimension
Abstract: I will give a brief survey of generalizations of covering dimension for
infinite dimensional separable metric spaces.
Marion Scheepers
How big can a Lindel\"of space be?
Abstract: We give a brief survey of some classical problems about the size of Lindel\"of spaces.
Selected recent results (with proofs, when they are not too technical) will be presented. Some of
the presented work is joint work with F.D. Tall (University of Toronto). It is anticipated that the
series will consist of three talks.
Andres Caicedo
BPFA and projective well-orderings of the reals
Abstract: I will sketch a proof of the following fact: If BPFA (the bounded proper forcing axiom) holds, and omega_1 = omega_1^L, then there is a (lightface) Sigma^1_3 well-ordering of the reals. The argument combines a coding technique of Caicedo-Velickovic with Friedman's `David trick.' This is joint work with Sy Friedman.
Previous seminars:
September 8
Masaru Kada
Galois-Tukey connection involving
sets of metrics
(joint work with Yasuo Yoshinobu)
Abstract: Woods proved that
the Stone-Cech compactification of a metrizable space X is approximated by the
collection of Smirnov compactifications for all
compatible metrics on X. As an improvement of Woods' Theorem, Kada, Tomoyasu
and Yoshinobu studied, for a metrizable space X, how many metrics we actually
need to approximate the Stone-Cech compactification by Smirnov compactifications.
After that, Todorcevic told us that the answers to such cardinality questions
should be naturally deduced from structural information of the set of compatible
metrics on the space, and so we should investigate the structure, not just
cardinalities, of the set of metrics.
I will present some recent results on this topic. I will show that the
structure of the set of compatible metrics of a separable metrizable space X is
nicely characterized using the notion of generalized Galois-Tukey connection.
September 15-22
Masaru Kada
How to amplify a metric, and how to
gauge the amplitude of a metric
Abstract: I will present a part of the proof of our
theorem, which provides a sequence of morphisms (in the sense of Galois-Tukey
connections) involving the order structure of the set of metrics on a locally
compact separable metrizable space. The key idea of the proof is a method to
"amplify" a fixed metric by an "amplitude" indicated by a strictly increasing
function, and to "gauge the amplitude" of a given metric using the fixed metric
as a base. I will try to explain the effectiveness of our assumption that our
space is locally compact and separable, and give some idea how to apply our
result for a separable (but not necessarily locally compact) metrizable space.
