Sam Ziegler : Complete left-invariant metrics for automorphism groups of models

Posted by Sam Ziegler , part of the Louise Hay Logic Seminar.

At

Dec. 5, 2013, 4 p.m.

In

SEO 427

Abstract

Any Polish group can be equipped with a compatible left-invariant metric; however, there may be no compatible left-invariant metric which is also complete. Groups which do have such a metric are known as CLI groups. In this talk, we will examine a theorem, due to Gao, characterizing when groups of the form $Aut(\mathcal{M})$ are CLI. It turns out that for such automorphism groups, CLI can be reformulated as a property of the Scott sentence of $\mathcal{M}$.