{
  "id": "1012.3508",
  "version": "v4",
  "published": "2010-12-16T03:33:37.000Z",
  "updated": "2011-08-16T00:57:02.000Z",
  "title": "Expansions of subfields of the real field by a discrete set",
  "authors": [
    "Philipp Hieronymi"
  ],
  "journal": "Fund. Math. 215 (2011) 167-175",
  "categories": [
    "math.LO"
  ],
  "abstract": "Let K be a subfield of the real field, D be a discrete subset of K and f : D^n -> K be a function such that f(D^n) is somewhere dense. Then (K,f) defines the set of integers. We present several applications of this result. We show that K expanded by predicates for different cyclic multiplicative subgroups defines the set of integers. Moreover, we prove that every definably complete expansion of a subfield of the real field satisfies an analogue of the Baire Category Theorem.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2011-08-16T00:57:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C64",
      "14P10",
      "54E52"
    ],
    "keywords": [
      "discrete set",
      "cyclic multiplicative subgroups defines",
      "real field satisfies",
      "baire category theorem",
      "definably complete expansion"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1012.3508H"
    }
  }
}