{
  "id": "2008.00268",
  "version": "v1",
  "published": "2020-08-01T14:13:58.000Z",
  "updated": "2020-08-01T14:13:58.000Z",
  "title": "Big Ramsey degrees of 3-uniform hypergraphs are finite",
  "authors": [
    "Martin Balko",
    "David Chodounský",
    "Jan Hubička",
    "Matěj Konečný",
    "Lluis Vena"
  ],
  "comment": "9 pages",
  "categories": [
    "math.CO",
    "cs.DM",
    "math.LO"
  ],
  "abstract": "Generalizing the passing number construction by Sauer, we give a short proof of the fact that the universal homogeneous 3-uniform hypergraph has finite big Ramsey degrees. Our proof is based on vector (or product) form of the Milliken's tree theorem and demonstrates a general method to carry existing results on structures in binary relational languages to higher arities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-01T14:13:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D10",
      "05C05",
      "05C65",
      "05C55",
      "05C80",
      "G.2.2",
      "F.4.1"
    ],
    "keywords": [
      "hypergraph",
      "finite big ramsey degrees",
      "binary relational languages",
      "millikens tree theorem",
      "general method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}