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.