{
  "id": "1410.2520",
  "version": "v1",
  "published": "2014-10-09T16:17:23.000Z",
  "updated": "2014-10-09T16:17:23.000Z",
  "title": "The topological pigeonhole principle for ordinals",
  "authors": [
    "Jacob Hilton"
  ],
  "comment": "22 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "Given a cardinal $\\kappa$ and a sequence $\\left(\\alpha_i\\right)_{i\\in\\kappa}$ of ordinals, we determine the least ordinal $\\beta$ such that the topological partition relation \\[\\beta\\rightarrow\\left(top\\,\\alpha_i\\right)^1_{i\\in\\kappa}\\] holds, including an independence result for one class of cases. Here the prefix \"$top$\" means that the homogeneous set must be of the correct homeomorphism class rather than the correct order type. The answer is linked to the non-topological pigeonhole principle of Milner and Rado.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-09T16:17:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E02"
    ],
    "keywords": [
      "correct homeomorphism class",
      "correct order type",
      "non-topological pigeonhole principle",
      "topological partition relation",
      "independence result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.2520H"
    }
  }
}