Submission date: 5 April 2024

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 SOP_3, TP_2, and 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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Full text arXiv 2404.04381: pdf, ps.