Submission date: 3 October 2017

Abstract:

For a finite lattice Λ, Λ-ultrametric spaces are a convenient language for describing structures equipped with a family of equivalence relations. When Λ is finite and distributive, there exists a generic Λ-ultrametric space, and we here identify a family of Ramsey expansions for that space. This then allows a description the universal minimal flow of its automorphism group, and also implies the Ramsey property for all known homogeneous finite-dimensional permutation structures, i.e. structures in a language of finitely many linear orders. A point of technical interest is that our proof involves classes with non-unary algebraic closure operations. As a byproduct of some of the concepts developed, we also arrive at a natural description of the known homogeneous finite-dimensional permutation structures, completing our previously begun “census”.

Mathematics Subject Classification: 03C13, 03C15, 03C50, 05D10, 37B05

Keywords and phrases:

Full text arXiv 1710.01193: pdf, ps.