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June 2009 Lowness for Kurtz randomness
Noam Greenberg, Joseph S. Miller
J. Symbolic Logic 74(2): 665-678 (June 2009). DOI: 10.2178/jsl/1243948333

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.

Citation

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Noam Greenberg. Joseph S. Miller. "Lowness for Kurtz randomness." J. Symbolic Logic 74 (2) 665 - 678, June 2009. https://doi.org/10.2178/jsl/1243948333

Information

Published: June 2009
First available in Project Euclid: 2 June 2009

zbMATH: 1168.03033
MathSciNet: MR2518817
Digital Object Identifier: 10.2178/jsl/1243948333

Subjects:
Primary: 03D80
Secondary: 68Q30

Rights: Copyright © 2009 Association for Symbolic Logic

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Vol.74 • No. 2 • June 2009
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