Devrim Pekmezci of UIC : Topics Seminar: NSOP_n theories for n > 1

Posted by Scott Mutchnik , part of the Logic Seminar.

At

Sept. 22, 2026, 2 p.m.

In

636 SEO

Abstract

We will have a research seminar this semester on NSOP_n theories for n > 1, assuming no theorems on the identity of NSOP_1 and also not assuming that n is an integer. Graduate students are particularly encouraged to attend. We will discuss straight definability and poset-definability of classification-theoretic properties--respectively, the meta-properties of being defined in terms of a pattern of consistency and inconsistency in a formula and its negation, and of being defined in terms of interpreting a partially ordered set embedding a fixed poset. We will then discuss the proof of Day and Mutchnik's result that the n-strict order property, SOP_n, is poset-definable and thus straightly definable for integers n > 3 (in addition to the previously known fact that SOP_1, SOP_2 and SOP_3 are even positively straightly definable.) This result resolves problems of Bailetti (who popularized straight definability, defined under different terminology by Shelah), and of Garcia and Mennuni (who introduced poset definability).