Phillip Wesolek : Constructible t.d.l.c. Polish groups and a question of Gao's

Posted by Phillip Wesolek , part of the Louise Hay Logic Seminar.

At

Feb. 6, 2014, 3 p.m.

In

SEO 427

Abstract

The class of constructible t.d.l.c. Polish groups is the class of t.d.l.c. Polish groups which are built from profinite and discrete groups by group extension and countable increasing union. We first explore closure properties of this class. We then use these closure properties to show the following fact: if there is a surjectively universal t.d.l.c. Polish group, then there is a constructible group which is surjectively universal for the class of constructible groups. This fact is a step in the direction of answering the following: (Gao) Is there a surjectively universal t.d.l.c. Polish group?