{
  "id": "math/0602415",
  "version": "v1",
  "published": "2006-02-20T20:21:06.000Z",
  "updated": "2006-02-20T20:21:06.000Z",
  "title": "Decidability of the Natural Numbers with the Almost-All Quantifier",
  "authors": [
    "David Marker",
    "Theodore A. Slaman"
  ],
  "categories": [
    "math.LO",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider the fragment F of first order arithmetic in which quantification is restricted to ''for all but finitely many.'' We show that the integers form an F-elementary substructure of the real numbers. Consequently, the F-theory of arithmetic is decidable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-02-20T20:21:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03F30"
    ],
    "keywords": [
      "natural numbers",
      "almost-all quantifier",
      "decidability",
      "first order arithmetic",
      "f-elementary substructure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......2415M"
    }
  }
}