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Computational randomness and lowness
Journal of Symbolic Logic 66 (3):1199-1205 (2001)
Abstract
We prove that there are uncountably many sets that are low for the class of Schnorr random reals. We give a purely recursion theoretic characterization of these sets and show that they all have Turing degree incomparable to 0'. This contrasts with a result of Kučera and Terwijn [5] on sets that are low for the class of Martin-Löf random realsOther Versions
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Citations of this work
Calibrating randomness.Rod Downey, Denis R. Hirschfeldt, André Nies & Sebastiaan A. Terwijn - 2006 - Bulletin of Symbolic Logic 12 (3):411-491.
Almost everywhere domination and superhighness.Stephen G. Simpson - 2007 - Mathematical Logic Quarterly 53 (4):462-482.
Randomness and computability: Open questions.Joseph S. Miller & André Nies - 2006 - Bulletin of Symbolic Logic 12 (3):390-410.
Lowness properties and approximations of the jump.Santiago Figueira, André Nies & Frank Stephan - 2008 - Annals of Pure and Applied Logic 152 (1):51-66.
References found in this work
The Degrees of Hyperimmune Sets.Webb Miller & D. A. Martin - 1968 - Mathematical Logic Quarterly 14 (7-12):159-166.
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