{
  "id": "1304.1380",
  "version": "v1",
  "published": "2013-04-04T14:41:30.000Z",
  "updated": "2013-04-04T14:41:30.000Z",
  "title": "Groups definable in two orthogonal sorts",
  "authors": [
    "Alessandro Berarducci",
    "Marcello Mamino"
  ],
  "comment": "18 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "This work can be thought as a contribution to the model theory of group extensions. We study the groups G which are interpretable in the disjoint union of two structures (seen as a two-sorted structure). We show that if one of the two structures is superstable of finite Lascar rank and the Lascar rank is definable, then G is an extension of a group internal to the (possibly) unstable sort by a definable subgroup internal to the stable sort. In the final part of the paper we show that if the unstable sort is an o-minimal expansion of the reals, then G has a natural Lie structure and the extension is a topological cover.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-04-04T14:41:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C45",
      "03C64",
      "22E99"
    ],
    "keywords": [
      "orthogonal sorts",
      "groups definable",
      "finite lascar rank",
      "unstable sort",
      "natural lie structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1304.1380B"
    }
  }
}