{
  "id": "math/9507213",
  "version": "v1",
  "published": "1995-07-26T00:00:00.000Z",
  "updated": "1995-07-26T00:00:00.000Z",
  "title": "On a Glimm -- Effros dichotomy and an Ulm--type classification in Solovay model",
  "authors": [
    "Vladimir Kanovei"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We prove that in Solovay model every OD equivalence E on reals either admits an OD reduction to the equality on the set of all countable (of length < omega_1) binary sequences, or continuously embeds E_0, the Vitali equivalence. If E is a Sigma_1^1 (resp. Sigma_1^2) relation then the reduction in the ``either'' part can be chosen in the class of all Delta_1 (resp. Delta_2) functions. The proofs are based on a topology generated by OD sets.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1995-07-26T00:00:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "solovay model",
      "ulm-type classification",
      "effros dichotomy",
      "od equivalence",
      "vitali equivalence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1995math......7213K"
    }
  }
}