{
  "id": "1405.0568",
  "version": "v2",
  "published": "2014-05-03T11:20:12.000Z",
  "updated": "2015-07-01T20:50:52.000Z",
  "title": "On Superstable Expansions of Free Abelian Groups",
  "authors": [
    "Daniel Palacin",
    "Rizos Sklinos"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We prove that $(\\Z,+,0)$ has no proper superstable expansions of finite Lascar rank. Nevertheless, this structure equipped with a predicate defining powers of a given natural number is superstable of Lascar rank $\\omega$. Additionally, our methods yield other superstable expansions such as $(\\Z,+,0)$ equipped with the set of factorial elements.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-05-03T11:20:12.000Z",
      "abstract": "We prove that $(\\mathbb Z,+,0)$ has no proper superstable expansions of finite Lascar rank. Nevertheless, we exhibit a superstable proper expansion.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-07-01T20:50:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C45"
    ],
    "keywords": [
      "free abelian groups",
      "finite lascar rank",
      "proper superstable expansions",
      "superstable proper expansion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.0568P"
    }
  }
}