{
  "id": "1701.07235",
  "version": "v1",
  "published": "2017-01-25T10:09:30.000Z",
  "updated": "2017-01-25T10:09:30.000Z",
  "title": "Recognizing the real line",
  "authors": [
    "A. M. W. Glass",
    "John S. Wilson"
  ],
  "comment": "13 pages. arXiv admin note: substantial text overlap with arXiv:1606.00312",
  "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 the automorphism group of the real line (in the language of groups) then $\\Omega$ and and the real line are isomorphic ordered sets. This improvement of a theorem of Gurevich and Holland is obtained as a consequence of a study of centralizers associated with certain transitive subgroups of Aut$(\\Omega,\\leq)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-25T10:09:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20B07",
      "06F15"
    ],
    "keywords": [
      "real line",
      "automorphism group",
      "recognizing",
      "isomorphic ordered sets",
      "first-order sentences"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}