Lowness for Kurtz randomness

Journal of Symbolic Logic 74 (2):665-678 (2009)
Abstract
We prove that degrees that are low for Kurtz randomness cannot be diagonally non-recursive. Together with the work of Stephan and Yu [16], this proves that they coincide with the hyperimmune-free non-DNR degrees, which are also exactly the degrees that are low for weak 1-genericity. We also consider Low(M, Kurtz), the class of degrees a such that every element of M is a-Kurtz random. These are characterised when M is the class of Martin-Löf random, computably random, or Schnorr random reals. We show that Low(ML, Kurtz) coincides with the non-DNR degrees, while both Low(CR, Kurtz) and Low(Schnorr, Kurtz) are exactly the non-high, non-DNR degrees
Keywords No keywords specified (fix it)
Categories (categorize this paper)
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
 
Download options
PhilPapers Archive


Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 9,357
External links
  •   Try with proxy.
  •   Try with proxy.
  •   Try with proxy.
  • Through your library Configure
    References found in this work BETA

    No references found.

    Citations of this work BETA
    Similar books and articles
    Joseph Berkovitz, Roman Frigg & Fred Kronz (2006). The Ergodic Hierarchy, Randomness and Hamiltonian Chaos. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 37 (4):661-691.
    Antony Eagle, Chance Versus Randomness. Stanford Encyclopedia of Philosophy.
    Roman Frigg (2006). The Ergodic Hierarchy, Randomness and Hamiltonian Chaos. Studies in History and Philosophy of Science Part B 37 (4):661-691.
    Antony Eagle (2005). Randomness Is Unpredictability. British Journal for the Philosophy of Science 56 (4):749-790.
    Rodney G. Downey & Evan J. Griffiths (2004). Schnorr Randomness. Journal of Symbolic Logic 69 (2):533 - 554.
    Analytics

    Monthly downloads

    Added to index

    2010-09-12

    Total downloads

    2 ( #258,148 of 1,088,428 )

    Recent downloads (6 months)

    1 ( #69,601 of 1,088,428 )

    How can I increase my downloads?

    My notes
    Sign in to use this feature


    Discussion
    Start a new thread
    Order:
    There  are no threads in this forum
    Nothing in this forum yet.