{
  "id": "2001.06513",
  "version": "v1",
  "published": "2020-01-17T20:12:32.000Z",
  "updated": "2020-01-17T20:12:32.000Z",
  "title": "The independence of Stone's Theorem from the Boolean Prime Ideal Theorem",
  "authors": [
    "Samuel M. Corson"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We give a permutation model in which Stone's Theorem (every metric space is paracompact) is false and the Boolean Prime Ideal Theorem (every ideal in a Boolean algebra extends to a prime ideal) is true. The erring metric space in our model attains only rational distances and is not metacompact. Transfer theorems give the comparable independence in the Zermelo-Fraenkel setting, answering a question of Good, Tree and Watson.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-17T20:12:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E25",
      "54A35",
      "54E35",
      "54D20"
    ],
    "keywords": [
      "boolean prime ideal theorem",
      "stones theorem",
      "independence",
      "boolean algebra extends",
      "rational distances"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}