{
  "id": "math/0102043",
  "version": "v1",
  "published": "2001-02-06T17:31:16.000Z",
  "updated": "2001-02-06T17:31:16.000Z",
  "title": "Universal graphs at the successor of a singular cardinal",
  "authors": [
    "Mirna Džamonja",
    "Saharon Shelah"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "The paper is concerned with the existence of a universal graph at the successor of a strong limit singular mu of cofinality aleph_0. Starting from the assumption of the existence of a supercompact cardinal, a model is built in which for some such mu there are mu^{++} graphs on mu^+ that taken jointly are universal for the graphs on mu^+, while 2^{mu^+}>> mu^{++} . The paper also addresses the general problem of obtaining a framework for consistency results at the successor of a singular strong limit starting from the assumption that a supercompact cardinal kappa exists. The result on the existence of universal graphs is obtained as a specific application of a more general method.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-02-06T17:31:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E35",
      "03E55",
      "03E75"
    ],
    "keywords": [
      "universal graph",
      "singular cardinal",
      "strong limit singular mu",
      "supercompact cardinal kappa",
      "singular strong limit"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......2043D"
    }
  }
}