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
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DOI 10.2178/jsl/1243948333
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References found in this work BETA

Computability and Randomness.André Nies - 2008 - Oxford, England: Oxford University Press.
Computability and Randomness.André Nies - 2008 - Oxford, England: Oxford University Press UK.
Calibrating Randomness.Rod Downey, Denis R. Hirschfeldt, André Nies & Sebastiaan A. Terwijn - 2006 - Bulletin of Symbolic Logic 12 (3):411-491.
Computational Randomness and Lowness.Sebastiaan A. Terwijn & Domenico Zambella - 2001 - Journal of Symbolic Logic 66 (3):1199-1205.
Mass Problems and Hyperarithmeticity.Joshua A. Cole & Stephen G. Simpson - 2007 - Journal of Mathematical Logic 7 (2):125-143.

View all 9 references / Add more references

Citations of this work BETA

Randomness and Lowness Notions Via Open Covers.Laurent Bienvenu & Joseph S. Miller - 2012 - Annals of Pure and Applied Logic 163 (5):506-518.
Ramsey-Type Graph Coloring and Diagonal Non-Computability.Ludovic Patey - 2015 - Archive for Mathematical Logic 54 (7-8):899-914.
Higher Kurtz Randomness.Bjørn Kjos-Hanssen, André Nies, Frank Stephan & Liang Yu - 2010 - Annals of Pure and Applied Logic 161 (10):1280-1290.
Martin-Löf Randomness and Galton–Watson Processes.David Diamondstone & Bjørn Kjos-Hanssen - 2012 - Annals of Pure and Applied Logic 163 (5):519-529.

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