{
  "id": "1605.00605",
  "version": "v1",
  "published": "2016-05-02T18:27:53.000Z",
  "updated": "2016-05-02T18:27:53.000Z",
  "title": "Universal graphs at $\\aleph_{ω_1+1}$",
  "authors": [
    "Jacob Davis"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "Starting from a supercompact cardinal we build a model in which $2^{\\aleph_{\\omega_1}}=2^{\\aleph_{\\omega_1+1}}=\\aleph_{\\omega_1+3}$ but there is a jointly universal family of size $\\aleph_{\\omega_1+2}$ of graphs on $\\aleph_{\\omega_1+1}$. The same technique will work for any uncountable cardinal in place of $\\omega_1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-02T18:27:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E35",
      "03E55",
      "03E75"
    ],
    "keywords": [
      "universal graphs",
      "supercompact cardinal",
      "jointly universal"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}