{
  "id": "1907.02769",
  "version": "v1",
  "published": "2019-07-05T11:02:39.000Z",
  "updated": "2019-07-05T11:02:39.000Z",
  "title": "A comparison of various analytic choice principles",
  "authors": [
    "Paul-Elliot Anglès d'Auriac",
    "Takayuki Kihara"
  ],
  "categories": [
    "math.LO",
    "cs.LO"
  ],
  "abstract": "We investigate computability theoretic and descriptive set theoretic contents of various kinds of analytic choice principles by performing detailed analysis of the Medvedev lattice of $\\Sigma^1_1$-closed sets. Among others, we solve an open problem on the Weihrauch degree of the parallelization of the $\\Sigma^1_1$-choice principle on the integers. Harrington's unpublished result on a jump hierarchy along a pseudo-well-ordering plays a key role in solving the problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-05T11:02:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "analytic choice principles",
      "comparison",
      "descriptive set theoretic contents",
      "medvedev lattice",
      "open problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}