Homogeneous 3-dimensional permutation structures

Abstract

We provide a classification of the homogeneous 3-dimensional permutation structures, i.e. homogeneous structures in a language of 3 linear orders, partially answering a question of Cameron. We also arrive at a natural description of all known homogeneous finite-dimensional permutation structures by modifying the language used in the construction from a previous paper, completing the "census" begun there.

30 pages, Journal version

References in corpus (1)

• Ramsey expansions of $\Lambda$-ultrametric spaces

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• $\Lambda$-ultrametric spaces and lattices of equivalence relations
• NIP omega-categorical structures: the rank 1 case
• Ramsey expansions of $\Lambda$-ultrametric spaces
• The classification of homogeneous finite-dimensional permutation structures
• Structural Ramsey Theory and the Extension Property for Partial Automorphisms