{
  "id": "1705.10582",
  "version": "v1",
  "published": "2017-05-30T12:39:14.000Z",
  "updated": "2017-05-30T12:39:14.000Z",
  "title": "Finite Ramsey degrees and Fraïssé expansions with the Ramsey property",
  "authors": [
    "Lionel Nguyen Van Thé"
  ],
  "comment": "5 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "By a result of Zucker, every Fra\\\"iss\\'e structure $\\bf F$ for which the elements of $\\mathrm{Age}(\\bf F)$ have finite Ramsey degrees admits a Fra\\\"iss\\'e precompact expansion $\\bf F^{*}$ whose age $\\mathrm{Age}(\\bf F^{*})$ has the Ramsey property. While the original method uses dynamics in spaces of ultrafilters, the purpose of the present short note is to provide a different proof, based on classical tools from Fra\\\"iss\\'e theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-30T12:39:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D10",
      "03C15",
      "54H20"
    ],
    "keywords": [
      "ramsey property",
      "finite ramsey degrees admits",
      "short note",
      "original method",
      "precompact expansion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}