{
  "id": "1111.0729",
  "version": "v3",
  "published": "2011-11-03T05:10:48.000Z",
  "updated": "2014-05-24T00:14:13.000Z",
  "title": "Logic for metric structures and the number of universal sofic and hyperlinear groups",
  "authors": [
    "Martino Lupini"
  ],
  "comment": "14 pages; accepted for publication by the Proceedings of the American Mathematical Society",
  "categories": [
    "math.LO"
  ],
  "abstract": "Using the model theory of metric structures, I give an alternative proof of the following result by Thomas: If the Continuum Hypothesis fails then there are power of the continuum many universal sofic groups up to isomorphism. This method is also applicable to universal hyperlinear groups, giving a positive answer to a question posed by Thomas.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-05-24T00:14:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C20",
      "03E35",
      "20F69",
      "16E50"
    ],
    "keywords": [
      "metric structures",
      "universal sofic groups",
      "universal hyperlinear groups",
      "continuum hypothesis fails",
      "model theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.0729L"
    }
  }
}