{
  "id": "1205.6916",
  "version": "v2",
  "published": "2012-05-31T08:32:44.000Z",
  "updated": "2012-10-16T11:42:53.000Z",
  "title": "On Variants of CM-triviality",
  "authors": [
    "Thomas Blossier",
    "Amador Martin-Pizarro",
    "Frank Olaf Wagner"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We introduce a generalization of CM-triviality relative to a fixed invariant collection of partial types, in analogy to the Canonical Base Property defined by Pillay, Ziegler and Chatzidakis which generalizes one-basedness. We show that, under this condition, a stable field is internal to the family, and a group of finite Lascar rank has a normal nilpotent subgroup such that the quotient is almost internal to the family.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-10-16T11:42:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cm-triviality",
      "finite lascar rank",
      "normal nilpotent subgroup",
      "canonical base property",
      "fixed invariant collection"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.6916B"
    }
  }
}