{
  "id": "1502.00573",
  "version": "v1",
  "published": "2015-02-02T18:39:41.000Z",
  "updated": "2015-02-02T18:39:41.000Z",
  "title": "Quantifier elimination in C*-algebras",
  "authors": [
    "Christopher J. Eagle",
    "Ilijas Farah",
    "Eberhard Kirchberg",
    "Alessandro Vignati"
  ],
  "categories": [
    "math.LO",
    "math.OA"
  ],
  "abstract": "Conjecturally, the only C*-algebras that admit elimination of quantifiers in continuous logic are $\\mathbb{C}, \\mathbb{C}^2$, $C($Cantor space$)$ and $M_2(\\mathbb{C})$. Concentrating on the noncommutative case, we prove that $M_2(\\mathbb C)$ is the only exact noncommutative C*-algebra whose theory admits elimination of quantifiers and that every other example is purely infinite and simple.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-02-02T18:39:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C10",
      "03C65",
      "03C90",
      "46L89",
      "46L05",
      "46M07"
    ],
    "keywords": [
      "quantifier elimination",
      "theory admits elimination",
      "admit elimination",
      "cantor space",
      "continuous logic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150200573E"
    }
  }
}