{
  "id": "1912.12962",
  "version": "v1",
  "published": "2019-12-30T15:20:56.000Z",
  "updated": "2019-12-30T15:20:56.000Z",
  "title": "Indiscernible pairs of countable sets of reals at a given projective level",
  "authors": [
    "Vladimir Kanovei",
    "Vassily Lyubetsky"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "Using an invariant modification of Jensen's \"minimal $\\varPi^1_2$ singleton\" forcing, we define a model of ZFC, in which, for a given $n\\ge2$, there exists a lightface $\\varPi^1_n$ unordered pair of non-OD (hence, OD-indiscernible) countable sets of reals, but there is no $\\varSigma^1_n$ unordered pairs of this kind.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-30T15:20:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E15",
      "03E35"
    ],
    "keywords": [
      "countable sets",
      "projective level",
      "indiscernible pairs",
      "unordered pair",
      "invariant modification"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}