Travis Nell : Distal and non-Distal Behavior

Posted by James Freitag , part of the Logic Seminar.

At

March 20, 2018, 3:30 p.m.

In

SEO 427

Abstract

Let $\mathcal R=(R;+,<,\ldots)$ be an o-minimal expansion of an ordered group in language $\mathcal L$. Consider $S\subset R$. In many cases the $\mathcal L \cup \{P\}$-structure $(\mathcal R, S)$, which interprets $P$ as membership in $S$ can be well understood. In these cases, one question that can be asked is when "stable" behavior can occur in such a structure. Distality, introduced by Pierre Simon in 2011, is a notion of a structure being "purely unstable". I will consider the case where $S$ is a dense $\mathcal L$-elementary substructure of $\mathcal R$. While these cases are non-distal, we will demonstrate a characterization of the stable behavior in such a structure.