{
  "id": "1311.0333",
  "version": "v1",
  "published": "2013-11-02T03:16:09.000Z",
  "updated": "2013-11-02T03:16:09.000Z",
  "title": "On the Normality of Numbers to Different Bases",
  "authors": [
    "Verónica Becher",
    "Theodore A. Slaman"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove independence of normality to different bases We show that the set of real numbers that are normal to some base is Sigma^0_4 complete in the Borel hierarchy of subsets of real numbers. This was an open problem, initiated by Alexander Kechris, and conjectured by Ditzen 20 years ago.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-11-02T03:16:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "real numbers",
      "borel hierarchy",
      "alexander kechris",
      "open problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1311.0333B"
    }
  }
}