Algebra Seminar talk
2025-03-14
Alberto Miguel-Gómez
Model-theoretic properties of hypertournaments
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. Time permitting, I will highlight some apparent similarities between this example and the generic triangle-free graph, and discuss some open questions coming out of this comparison.