{
  "id": "1308.1696",
  "version": "v1",
  "published": "2013-08-07T20:55:35.000Z",
  "updated": "2013-08-07T20:55:35.000Z",
  "title": "An Easton-like Theorem for Zermelo-Fraenkel Set Theory Without Choice (Preliminary Report)",
  "authors": [
    "Anne Fernengel",
    "Peter Koepke"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "By Easton's theorem one can force the exponential function on regular cardinals to take rather arbitrary cardinal values provided monotonicity and Koenig's lemma are respected. In models without choice we employ a \"surjective\" version of the exponential function. We then prove a choiceless Easton's theorem: one can force the surjective exponential function on all infinite cardinals to take arbitrary cardinal values, provided monotonicity and Cantor's theorem are satisfied, irrespective of cofinalities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-08-07T20:55:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "zermelo-fraenkel set theory",
      "preliminary report",
      "easton-like theorem",
      "exponential function",
      "arbitrary cardinal values"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1308.1696F"
    }
  }
}