{
  "id": "1201.4909",
  "version": "v3",
  "published": "2012-01-24T03:36:20.000Z",
  "updated": "2013-10-20T20:44:30.000Z",
  "title": "Remarks on countable tightness",
  "authors": [
    "Marion Scheepers"
  ],
  "comment": "Extended from 12 pages to 23 pages. Newly extended to 27 pages",
  "categories": [
    "math.GN",
    "math.LO"
  ],
  "abstract": "Countable tightness may be destroyed by countably closed forcing. We characterize the indestructibility of countable tightness under countably closed forcing by combinatorial statements similar to the ones Tall used to characterize indestructibility of the Lindelof property under countably closed forcing. We consider the behavior of countable tightness in generic extensions obtained by adding Cohen reals. We show that certain classes of well-studied topological spaces are indestructibly countably tight. Stronger versions of countable tightness, including selective versions of separability, are further explored.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-10-20T20:44:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E05",
      "03E35",
      "54A35",
      "54D65"
    ],
    "keywords": [
      "countable tightness",
      "countably closed forcing",
      "combinatorial statements similar",
      "lindelof property",
      "generic extensions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1201.4909S"
    }
  }
}