Scott Mutchnik : Reading seminar

Posted by Scott Mutchnik , part of the Logic Seminar.

At

Feb. 24, 2026, 2 p.m.

In

427 SEO

Abstract

Following our discussion of the proof of Saracino's theorem, stating that every countably categorical theory has a model companion, we give an application. We prove Bodor, Bodirsky and Marimon's recent theorem that, for any theory T, an existential formula exhibiting SOP_n in the model companion of T (when well-defined) exhibits SOP_n in T. We then use this to prove our result with Gabriel Day that, if NSOP_2 is equal to NSOP_3, then for any countably categorical theory T and formula φ(x,y) exhibiting SOP_2 in T, some ∃∀-formula in φ(x,y) exhibits SOP_3 in T.