Abstract

We provide a model-theoretic classification of the countable homogeneous $H_4$-free $3$-hypertournament studied by Cherlin, Hubička, Konečný, and Nešetřil. Our main result is that the theory of this structure is ${\text{ SOP}}_3$, ${\text{ TP}}_2$, and ${\text{ NSOP}}_4$. We offer two proofs of this fact: one is a direct proof, and the other employs part of the abstract machinery recently developed by Mutchnik.

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Mathematical Subject Classification

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