{
  "id": "1903.08041",
  "version": "v1",
  "published": "2019-03-19T15:06:07.000Z",
  "updated": "2019-03-19T15:06:07.000Z",
  "title": "Countably compact groups and sequential order",
  "authors": [
    "Dmitri Shakhmatov",
    "Alexander Shibakov"
  ],
  "categories": [
    "math.GN"
  ],
  "abstract": "We use $\\diamondsuit$ to construct, for every $\\alpha\\leq\\omega_1$ a sequential countably compact topological group of sequential order $\\alpha$. This establishes the independence of the existence of sequential countably compact non Fr\\'echet groups from the usual axioms of ZFC and answers several questions of D.~Shakhmatov.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-19T15:06:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "countably compact groups",
      "sequential order",
      "sequential countably compact non frechet",
      "countably compact non frechet groups",
      "sequential countably compact topological group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}