{
  "id": "math/0305036",
  "version": "v1",
  "published": "2003-05-01T16:30:02.000Z",
  "updated": "2003-05-01T16:30:02.000Z",
  "title": "On relatively analytic and Borel subsets",
  "authors": [
    "Arnold W. Miller"
  ],
  "comment": "LaTeX2e 10 pages available at http://www.math.wisc.edu/~miller/res/index.html",
  "categories": [
    "math.LO"
  ],
  "abstract": "Define z to be the smallest cardinality of a function f:X->Y with X and Y sets of reals such that there is no Borel function g extending f. In this paper we prove that it is relatively consistent with ZFC to have b<z where b is, as usual, smallest cardinality of an unbounded family in w^w. This answers a question raised by Zapletal. We also show that it is relatively consistent with ZFC that there exists a set of reals X such that the Borel order of X is bounded but there exists a relatively analytic subset of X which is not relatively coanalytic. This answers a question of Mauldin.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-05-01T16:30:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E35",
      "03E17",
      "03E15"
    ],
    "keywords": [
      "borel subsets",
      "smallest cardinality",
      "relatively consistent",
      "borel function",
      "relatively analytic subset"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......5036M"
    }
  }
}