Roland Walker : Distality Rank

Posted by James Freitag , part of the Logic Seminar.

At

Oct. 29, 2019, 3:30 p.m.

In

427 SEO

Abstract

We develop distality rank as a property of first-order theories and give examples for each rank $m$ such that $1\leq m \leq \omega$. For NIP theories, we show that distality rank is invariant under base change. We also define a generalization of type orthogonality called $m$-determinacy and show that theories of distality rank $m$ require certain products to be $m$-determined. Furthermore, for NIP theories, this behavior characterizes distality rank $m$.