{
  "id": "1306.4940",
  "version": "v5",
  "published": "2013-06-20T17:34:38.000Z",
  "updated": "2014-06-18T20:35:25.000Z",
  "title": "Weak Rudin-Keisler reductions on projective ideals",
  "authors": [
    "Konstantinos A. Beros"
  ],
  "comment": "11 pages",
  "categories": [
    "math.LO",
    "math.GR"
  ],
  "abstract": "We consider a slightly modified form of the standard Rudin-Keisler order on ideals and demonstrate the existence of complete (with respect to this order) ideals in various projective classes. Using our methods, we obtain a simple proof of Hjorth's theorem on the existence of a complete $\\mathbf \\Pi^1_1$ equivalence relation. Our proof of Hjorth's theorem enables us (under PD) to generalize his result to the classes of $\\mathbf \\Pi^1_{2n+1}$ equivalence relations.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2014-06-18T20:35:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E15",
      "03E60",
      "03E05",
      "28A05"
    ],
    "keywords": [
      "weak rudin-keisler reductions",
      "projective ideals",
      "equivalence relation",
      "hjorths theorem enables",
      "standard rudin-keisler order"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1306.4940B"
    }
  }
}