{
  "id": "1003.5983",
  "version": "v1",
  "published": "2010-03-31T07:05:56.000Z",
  "updated": "2010-03-31T07:05:56.000Z",
  "title": "Complexity of Ramsey null sets",
  "authors": [
    "Marcin Sabok"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We show that the set of codes for Ramsey positive analytic sets is $\\mathbf{\\Sigma}^1_2$-complete. This is a one projective-step higher analogue of the Hurewicz theorem saying that the set of codes for uncountable analytic sets is $\\mathbf{\\Sigma}^1_1$-complete. This shows a close resemblance between the Sacks forcing and the Mathias forcing. In particular, we get that the $\\sigma$-ideal of Ramsey null sets is not ZFC-correct. This solves a problem posed by Ikegami, Pawlikowski and Zapletal.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-03-31T07:05:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E15",
      "28A05",
      "54H05"
    ],
    "keywords": [
      "ramsey null sets",
      "complexity",
      "ramsey positive analytic sets",
      "projective-step higher analogue",
      "close resemblance"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1003.5983S"
    }
  }
}