Series: Logic Seminar
Speaker: Stephen G. Simpson (Penn State, Mathematics)
Title: Separation Principles in Logic and Analysis
Date: Tuesday, September 8, 1998
Time: 2:30 PM
Place: 113 McAllister Building
Abstract:
We consider separation principles from diverse areas of mathematics
and mathematical logic. In functional analysis, there is the
geometrical form of the Hahn-Banach theorem, giving conditions under
which two disjoint convex sets can be separated by a hyperplane. In
descriptive set theory, there is Lusin's theorem which says that two
disjoint analytic sets can be separated by a Borel set. In subsystems
of second order arithmetic, there are the Sigma^0_1 and Sigma^1_1
separation principles. We use reverse mathematics to tie all these
topics together.