{
  "id": "1809.00922",
  "version": "v1",
  "published": "2018-09-04T12:48:44.000Z",
  "updated": "2018-09-04T12:48:44.000Z",
  "title": "Proof of a Conjecture of Galvin",
  "authors": [
    "Dilip Raghavan",
    "Stevo Todorcevic"
  ],
  "comment": "22 pages, Submitted",
  "categories": [
    "math.LO",
    "math.CO"
  ],
  "abstract": "We prove that if the set of unordered pairs of real numbers is colored by finitely many colors, there is a set of reals homeomorphic to the rationals whose pairs have at most two colors. Our proof uses large cardinals and it verifies a conjecture of Galvin from the 1970s. We extend this result to an essentially optimal class of topological spaces in place of the reals.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-04T12:48:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "conjecture",
      "large cardinals",
      "real numbers",
      "essentially optimal class",
      "reals homeomorphic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}