Series: Penn State Logic Seminar

Date: Tuesday, October 23, 2001

Time: 2:30 - 3:45 PM

Place: 306 Boucke Building

Speaker: Stephen G. Simpson, Mathematics, Penn State

Title: New Directions in Descriptive Set Theory

Abstract: 

Let X be a Polish space, and let E be an analytic equivalence relation
on X.  The space of equivalence classes X/E is known as a singular
space.  Note that many important non-Polish spaces are singular
spaces.  For example, the orbit space of a Polish group action on a
Polish space is a singular space.  An active direction in descriptive
set theory is the classification of singular spaces up to mutual Borel
embeddability.  X/E is said to be Borel embeddable into Y/F if there
exists a Borel map f:X-->Y such that, for all x,y in X, xEy iff
f(x)Ff(y).  This talk is based on the survey paper of the same title
by A. Kechris, in the Bulletin of Symbolic Logic, volume 5, 1999,
pages 161-174.