{
  "id": "1110.5365",
  "version": "v3",
  "published": "2011-10-24T22:20:49.000Z",
  "updated": "2012-07-26T15:17:03.000Z",
  "title": "The failure of GCH at a degree of supercompactness",
  "authors": [
    "Brent Cody"
  ],
  "journal": "Mathematical Logic Quarterly, 58(1-2): 83-94, 2012",
  "categories": [
    "math.LO"
  ],
  "abstract": "We determine the large cardinal consistency strength of the existence of a $\\lambda$-supercompact cardinal $\\kappa$ such that GCH fails at $\\lambda$. Indeed, we show that the existence of a $\\lambda$-supercompact cardinal $\\kappa$ such that $2^\\lambda \\geq \\theta$ is equiconsistent with the existence of a $\\lambda$-supercompact cardinal that is also $\\theta$-tall. We also prove some basic facts about the large cardinal notion of tallness with closure.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-07-26T15:17:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E55",
      "03E35"
    ],
    "keywords": [
      "supercompact cardinal",
      "supercompactness",
      "large cardinal consistency strength",
      "large cardinal notion",
      "gch fails"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1110.5365C"
    }
  }
}