{
  "id": "1710.01193",
  "version": "v1",
  "published": "2017-10-03T14:53:21.000Z",
  "updated": "2017-10-03T14:53:21.000Z",
  "title": "Ramsey expansions of $Λ$-ultrametric spaces",
  "authors": [
    "Samuel Braunfeld"
  ],
  "categories": [
    "math.LO",
    "math.CO"
  ],
  "abstract": "For a finite lattice $\\Lambda$, $\\Lambda$-ultrametric spaces are a convenient language for describing structures equipped with a family of equivalence relations. When $\\Lambda$ is finite and distributive, there exists a generic $\\Lambda$-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\".",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-03T14:53:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C13",
      "03C15",
      "03C50",
      "05D10",
      "37B05"
    ],
    "keywords": [
      "ultrametric space",
      "ramsey expansions",
      "homogeneous finite-dimensional permutation structures",
      "non-unary algebraic closure operations",
      "universal minimal flow"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}