Ernest Schimmerling

Mathematical logic seminar - February 3, 2004

Time: 12 - 1:30 p.m.

Room: Wean Hall 7220

Speaker: Paul Gartside
Assistant Professor
Department of Mathematics
University of Pittsburgh

Title: Polish groups strive for freedom, but never make it ...

Abstract:    First we consider the problem of when a Polish topological group is `almost free' in the sense that randomly chosen elements of the group generate a free subgroup, and when a Polish group has a dense free subgroup. Applications are given to automorphism groups of first order structures and other Polish groups. (Joint work with Robin Knight.)

Then we turn to the question of whether a Polish group can itself be a free group. Except in the trivial case of a countable free group with the discrete topology the answer is `no'. This last result was independently proved by Shelah.