{
  "id": "1408.4188",
  "version": "v1",
  "published": "2014-08-19T01:42:24.000Z",
  "updated": "2014-08-19T01:42:24.000Z",
  "title": "Small universal families of graphs on $\\aleph_{ω+1}$",
  "authors": [
    "James Cummings",
    "Mirna Džamonja",
    "Charles Morgan"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We prove that it is consistent that $\\aleph_\\omega$ is strong limit, $2^{\\aleph_\\omega}$ is large and the universality number for graphs on $\\aleph_{\\omega+1}$ is small. The proof uses Prikry forcing with interleaved collapsing.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-19T01:42:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E35"
    ],
    "keywords": [
      "small universal families",
      "strong limit",
      "universality number",
      "consistent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1408.4188C"
    }
  }
}