Alberto Miguel Gómez : An NSOP4 structure without stationarity

Posted by Gabriel Conant , part of the Logic Seminar.

At

Sept. 24, 2024, 4 p.m.

In

636 SEO

Abstract

3-hypertournaments are combinatorial structures that generalize tournaments to the ternary relational case in a similar way that 3-hypergraphs generalize graphs. Recently, Cherlin, Hubička, Konečny, and Nešetřil have identified a countable homogeneous 3-hypertournament with some wild behavior from the structural-Ramsey-theoretic point of view. In this talk, I will show that this behavior has a model-theoretic counterpart: namely, its theory is strictly NSOP4. Furthermore, the usual criteria from the literature do not apply in this case, making this a novel example of an NSOP4 theory. In this talk, I will discuss the proof of this fact and how it relates to the other known examples of NSOP4 in light of recent developments in the area.