{
  "id": "1503.06045",
  "version": "v1",
  "published": "2015-03-20T11:56:35.000Z",
  "updated": "2015-03-20T11:56:35.000Z",
  "title": "Notes on a model theory of quantum 2-torus for generic q",
  "authors": [
    "Masanori Itai",
    "Boris Zilber"
  ],
  "comment": "17 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "We describe a structure over the complex numbers associated with the non-commutative algebra Aq called quantum 2-tori. These turn out to have uncountably categorical L_omega1,omega-theory, and are similar to other pseudo-analytic structures considered by the second author. The first-order theory of a quantum torus for generic q interprets arithmetic and so is unstable and undecidable. But certain interesting reduct of the structure, a quantum line bundle, is superstable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-20T11:56:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C30",
      "03C45",
      "03C50"
    ],
    "keywords": [
      "model theory",
      "quantum line bundle",
      "first-order theory",
      "pseudo-analytic structures",
      "second author"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}