{
  "id": "1102.5578",
  "version": "v2",
  "published": "2011-02-28T02:41:28.000Z",
  "updated": "2015-12-24T09:39:49.000Z",
  "title": "Existentially closed locally finite groups",
  "authors": [
    "Saharon Shelah"
  ],
  "categories": [
    "math.LO",
    "math.GR"
  ],
  "abstract": "We investigate this class of groups originally called ulf (universal locally finite groups) of cardinality lambda. We prove that for every locally finite group G there is a canonical existentially closed extension of the same cardinality, unique up to isomorphism and increasing with G. Also we get, e.g., existence of complete members (i.e., with no non-inner automorphisms) in many cardinals (provably in ZFC). We also get a parallel to stability theory in the sense of investigating definable types though the class is very unstable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-02-28T02:41:28.000Z",
      "abstract": "We investigate this class of groups originally called ulf (universal locally finite groups) of cardinality lambda . We prove that for every locally finite group G there is a canonical existentially closed extention of the same cardinality, unique up to isomorphism and increasing with G . Also we get, e.g. existence of complete members (i.e. with no non-inner automorphisms) in many cardinals (provably in ZFC). We also get a parallel to stability theory in the sense of investigating definable types.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-12-24T09:39:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C55",
      "03C50",
      "03C60"
    ],
    "keywords": [
      "existentially closed locally finite groups",
      "universal locally finite groups",
      "cardinality lambda",
      "stability theory",
      "complete members"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1102.5578S"
    }
  }
}