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Asian Initiative for Infinity (AII) Graduate Summer School
(20 Jun - 17 Jul 2012)
Jointly funded by the John Templeton Foundation
~ Abstracts ~
Continuous reducibility for the real line
Daisuke Ikegami, University of California at Berkeley, USA
Given a topological space X and subsets A, B of X, A is continuously reducible to B if there is a continuous function f from X to itself such that A = f^{-1} (B).
Continuous reducibility for the Baire space has been extensively investigated by set theorists in California and it enjoys many nice properties (e.g., the order on Borel sets is semi-linear and well-founded). In this talk, we study the continuous reducibility for the real line and show that it is totally different from the one for the Baire space. In fact, one can embed P(omega) / fin into the reducibility structure on Borel subsets of the real line.
This is joint work with Philipp Schlicht and Hisao Tanaka.
« Back... Borel combinatorics and recursion theory
Andrew Scott Marks, University of California at Berkeley, USA
We settle several questions of Borel combinatorics related to matchings and graph colorings of n-regular Borel graphs. The solution to these problems is motivated by an investigation of the position of equivalence relations from recursion theory in the hierarchy of countable Borel equivalence relations.
« Back... Applications of MM
Stevo Todorcevic, University of Toronto, Canada
This will be an attempt for a comprehensive introduction to applications of Forcing Axioms such as, for example, the Proper Forcing Axiom or Martin's Maximum. Thus, we shall try to give an overview of the most important methods of constructing ccc, proper, semi-proper, and stationary preserving forcing notions.
« Back... Delta_1 definablity of nonstationary ideal
Liuzhen Wu, University of Vienna, Austria
I will present some basic facts concerning the role of non-stationary ideal in higher descriptive set theory. I will also mention some recently consistency result on the definablity of nonstationary ideal.
This is a joint work with Sy. Friedman.
« Back...
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