{
  "id": "1312.0586",
  "version": "v2",
  "published": "2013-12-02T20:40:44.000Z",
  "updated": "2017-06-07T15:34:24.000Z",
  "title": "The free group does not have the finite cover property",
  "authors": [
    "Rizos Sklinos"
  ],
  "comment": "23 pages, to appear in the Israel J. Math",
  "categories": [
    "math.LO",
    "math.GR",
    "math.GT"
  ],
  "abstract": "We prove that the first order theory of nonabelian free groups eliminates the \"there exists infinitely many\" quantifier (in eq). Equivalently, since the theory of nonabelian free groups is stable, it does not have the finite cover property. We also extend our results to torsion-free hyperbolic groups under some conditions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-12-02T20:40:44.000Z",
      "title": "Torsion-free hyperbolic groups and the finite cover property",
      "abstract": "We prove that the first order theory of non abelian free groups eliminates the \"there exists infinitely many\" quantifier (in eq). Equivalently, since the theory of non abelian free groups is stable, it does not have the finite cover property. We also extend our results to torsion-free hyperbolic groups under some conditions.",
      "comment": "30 pages, 8 figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2017-06-07T15:34:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite cover property",
      "torsion-free hyperbolic groups",
      "non abelian free groups eliminates",
      "first order theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.0586S"
    }
  }
}