{
  "id": "0905.4875",
  "version": "v1",
  "published": "2009-05-29T14:21:34.000Z",
  "updated": "2009-05-29T14:21:34.000Z",
  "title": "How can we recognize potentially ${\\bfΠ}^0_ξ$ subsets of the plane?",
  "authors": [
    "Dominique Lecomte"
  ],
  "categories": [
    "math.LO",
    "math.CT",
    "math.GN"
  ],
  "abstract": "Let $\\xi\\geq 1$ be a countable ordinal. We study the Borel subsets of the plane that can be made ${\\bf\\Pi}^0_\\xi$ by refining the Polish topology on the real line. These sets are called potentially ${\\bf\\Pi}^0_\\xi$. We give a Hurewicz-like test to recognize potentially ${\\bf\\Pi}^0_\\xi$ sets.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-05-29T14:21:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E15",
      "54H05"
    ],
    "keywords": [
      "real line",
      "borel subsets",
      "polish topology"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0905.4875L"
    }
  }
}