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Lowness for the class of Schnorr random sets
Notre Dame Journal of Formal Logic 35 (3):647-657 (2005)
Abstract
We answer a question of Ambos-Spies and Kuˇcera in the affirmative. They asked whether, when a real is low for Schnorr randomness, it is already low for Schnorr tests.Author's Profile
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Reviewed Work(s): Lowness properties and randomness. Advances in Mathematics, vol. 197 by André Nies; Lowness for the class of Schnorr random reals. SIAM Journal on Computing, vol. 35 by Bjørn Kjos-Hanssen; André Nies; Frank Stephan; Lowness for Kurtz randomness. The Journal of Symbolic Logic, vol. 74 by Noam Greenberg; Joseph S. Miller; Randomness and lowness notions via open covers. Annals of Pure and Applied Logic, vol. 163 by Laurent Bienvenu; Joseph S. Miller; Relativizations of randomness and genericity notions. The Bulletin of the London Mathematical Society, vol. 43 by Johanna N. Y. Franklin; Frank Stephan; Liang Yu; Randomness notions and partial relativization. Israel Journal of Mathematics, vol. 191 by George Barmpalias; Joseph S. Miller; André Nies. [REVIEW]Johanna N. Y. Franklin - forthcoming - Association for Symbolic Logic: The Bulletin of Symbolic Logic.
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Citations of this work
Randomness and computability: Open questions.Joseph S. Miller & André Nies - 2006 - Bulletin of Symbolic Logic 12 (3):390-410.
Lowness for Kurtz randomness.Noam Greenberg & Joseph S. Miller - 2009 - Journal of Symbolic Logic 74 (2):665-678.
Randomness and lowness notions via open covers.Laurent Bienvenu & Joseph S. Miller - 2012 - Annals of Pure and Applied Logic 163 (5):506-518.
Truth-table Schnorr randomness and truth-table reducible randomness.Kenshi Miyabe - 2011 - Mathematical Logic Quarterly 57 (3):323-338.
Π 1 0 Classes, Peano Arithmetic, Randomness, and Computable Domination.David E. Diamondstone, Damir D. Dzhafarov & Robert I. Soare - 2010 - Notre Dame Journal of Formal Logic 51 (1):127-159.
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