Ramsey expansions of $Λ$-ultrametric spaces
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arXiv
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| Format: | Preprint |
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2017
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| _version_ | 1866908665998475264 |
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| author | Braunfeld, Samuel |
| author_facet | Braunfeld, Samuel |
| contents | 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". |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1710_01193 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Ramsey expansions of $Λ$-ultrametric spaces Braunfeld, Samuel Logic Combinatorics 03C13, 03C15, 03C50, 05D10, 37B05 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". |
| title | Ramsey expansions of $Λ$-ultrametric spaces |
| topic | Logic Combinatorics 03C13, 03C15, 03C50, 05D10, 37B05 |
| url | https://arxiv.org/abs/1710.01193 |