{
  "id": "1203.6299",
  "version": "v3",
  "published": "2012-03-28T15:40:39.000Z",
  "updated": "2012-09-13T21:54:56.000Z",
  "title": "Interpreting the projective hierarchy in expansions of the real line",
  "authors": [
    "Philipp Hieronymi",
    "Michael Tychonievich"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We give a criterion when an expansion of the ordered set of real numbers defines the image of the expansion of the real field by the set of natural numbers under a semialgebraic injection. In particular, we show that for a non-quadratic irrational number a, the expansion of the ordered Q(a)-vector space of real numbers by the set of natural numbers defines multiplication on the real numbers.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-09-13T21:54:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "real line",
      "projective hierarchy",
      "natural numbers defines multiplication",
      "real numbers defines",
      "non-quadratic irrational number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1203.6299H"
    }
  }
}