Logic Seminar
Alberto Miguel Gómez
Imperial College London
An NSOP4 structure without stationarity
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.
Tuesday September 24, 2024 at 4:00 PM in 636 SEO