{
  "id": "math/0506019",
  "version": "v2",
  "published": "2005-06-01T13:10:18.000Z",
  "updated": "2005-11-14T03:38:32.000Z",
  "title": "Uniform almost everywhere domination",
  "authors": [
    "Peter Cholak",
    "Joseph Miller",
    "Noam Greenberg"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We explore the interaction between Lebesgue measure and dominating functions. We show, via both a priority construction and a forcing construction, that there is a function of incomplete degree that dominates almost all degrees. This answers a question of Dobrinen and Simpson, who showed that such functions are related to the proof-theoretic strength of the regularity of Lebesgue measure for $G_\\delta$ sets. Our constructions essentially settle the reverse mathematical classification of this principle. Revised Nov 13, 2005. Minor corrections made.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-11-14T03:38:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03D28",
      "03D30",
      "03D60"
    ],
    "keywords": [
      "lebesgue measure",
      "domination",
      "minor corrections",
      "priority construction",
      "proof-theoretic strength"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......6019C"
    }
  }
}