{
  "id": "1606.00312",
  "version": "v1",
  "published": "2016-06-01T14:46:23.000Z",
  "updated": "2016-06-01T14:46:23.000Z",
  "title": "The first-order theory of $\\ell$-permutation groups",
  "authors": [
    "A. M. W. Glass",
    "John S. Wilson"
  ],
  "comment": "23 pages, 0 figures",
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $(\\Omega, \\leq)$ be a totally ordered set. We prove that if $\\Aut(\\Omega,\\leq)$ is transitive and satisfies the same first-order sentences as $\\Aut(\\RR,\\leq)$ (in the language of lattice-ordered groups) then $\\Omega$ and $\\RR$ are isomorphic ordered sets. This improvement of a theorem of Gurevich and Holland is obtained as one of many consequences of a study of centralizers and coloured chains associated with certain transitive subgroups of $\\Aut(\\Omega,\\leq)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-01T14:46:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "permutation groups",
      "first-order theory",
      "first-order sentences",
      "isomorphic ordered sets",
      "totally ordered set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}