{
  "id": "1601.07099",
  "version": "v1",
  "published": "2016-01-26T17:12:54.000Z",
  "updated": "2016-01-26T17:12:54.000Z",
  "title": "Decidability and classification of the theory of integers with primes",
  "authors": [
    "Itay Kaplan",
    "Saharon Shelah"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We show that under Dickson's conjecture about the distribution of primes in the natural numbers, the theory Th(Z,+,1,0,Pr) where Pr is a predicate for the prime numbers and their negations is decidable, unstable and supersimple. This is in contrast with Th(Z,+,0,Pr,<) which is known to be undecidable by the works of Jockusch, Bateman and Woods.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-26T17:12:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C45",
      "03F30",
      "03B25",
      "11A41"
    ],
    "keywords": [
      "decidability",
      "classification",
      "dicksons conjecture",
      "natural numbers",
      "prime numbers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160107099K"
    }
  }
}