Logic Seminar
Travis Nell
UIUC
Distal and non-Distal Behavior
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.
Tuesday March 20, 2018 at 3:30 PM in SEO 427