{
  "id": "1408.2282",
  "version": "v1",
  "published": "2014-08-10T23:42:42.000Z",
  "updated": "2014-08-10T23:42:42.000Z",
  "title": "On a conjecture of Dobrinen and Simpson concerning almost everywhere domination",
  "authors": [
    "Stephen Binns",
    "Bjørn Kjos-Hanssen",
    "Manuel Lerman",
    "Reed Solomon"
  ],
  "journal": "Journal of Symbolic Logic 71 (2006), no. 1, 119--136",
  "doi": "10.2178/jsl/1140641165",
  "categories": [
    "math.LO"
  ],
  "abstract": "The notions of almost everywhere (a.e.) domination and its uniform version were introduced and studied in reverse mathematics. This paper studies these notions from a recursion-theoretic point of view and explore their connections to notions such as randomness and genericity. It is shown that if $Z$ is a.e. dominating then each $1$-$Z$-random is $2$-random. In other words, $0'\\leq_{\\rm LR} Z$ for every a.e. dominating $Z$, where ${\\rm LR}$ denotes low-for-random reducibility. Other results and corollaries are also given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-10T23:42:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "simpson concerning",
      "domination",
      "conjecture",
      "denotes low-for-random reducibility",
      "paper studies"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1408.2282B"
    }
  }
}