{
  "id": "1210.5603",
  "version": "v1",
  "published": "2012-10-20T11:10:12.000Z",
  "updated": "2012-10-20T11:10:12.000Z",
  "title": "One Dimensional T.T.T Structures",
  "authors": [
    "Daniel Lowengrub"
  ],
  "comment": "26 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "In this paper we analyze the relationship between o-minimal structures and the notion of \\omega -saturated one dimensional t.t.t structures. We prove that if removing any point from such a structure splits it into more than one definably connected component then it must be a one dimensional simplex of a finite number of o-minimal structures. In addition, we show that even if removing points doesn't split the structure, additional topological assumptions ensure that the structure is locally o-minimal. As a corollary we obtain the result that if an \\omega -saturated one dimensional t.t.t structure admits a topological group structure then it is locally o-minimal. We also prove that the number of connected components in a definable family is uniformally bounded which implies that an elementary extension of an \\omega -saturated one dimensional t.t.t structure is t.t.t as well.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-10-20T11:10:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C64"
    ],
    "keywords": [
      "o-minimal structures",
      "locally o-minimal",
      "connected component",
      "additional topological assumptions ensure",
      "structure admits"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.5603L"
    }
  }
}