Randomness and lowness notions via open covers

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Annals of Pure and Applied Logic 163 (5):506-518 (2012)
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10.1016/j.apal.2011.06.009

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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.
Lowness and $\Pi _{2}^{0}$ Nullsets.Rod Downey, Andre Nies, Rebecca Weber & Liang Yu - 2006 - Journal of Symbolic Logic 71 (3):1044 - 1052.
Lowness for Kurtz randomness.Noam Greenberg & Joseph S. Miller - 2009 - Journal of Symbolic Logic 74 (2):665-678.
Hyperimmune-free degrees and Schnorr triviality.Johanna N. Y. Franklin - 2008 - Journal of Symbolic Logic 73 (3):999-1008.
Randomness and computability: Open questions.Joseph S. Miller & André Nies - 2006 - Bulletin of Symbolic Logic 12 (3):390-410.
Promptness Does Not Imply Superlow Cuppability.David Diamondstone - 2009 - Journal of Symbolic Logic 74 (4):1264 - 1272.
Combinatorial properties of filters and open covers for sets of real numbers.Claude Laflamme & Marion Scheepers - 1999 - Journal of Symbolic Logic 64 (3):1243-1260.
Benign cost functions and lowness properties.Noam Greenberg & André Nies - 2011 - Journal of Symbolic Logic 76 (1):289 - 312.
Chance versus Randomness.Antony Eagle - 2010 - Stanford Encyclopedia of Philosophy.

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Citations of this work

Lowness for Difference Tests.David Diamondstone & Johanna N. Y. Franklin - 2014 - Notre Dame Journal of Formal Logic 55 (1):63-73.
Deep classes.Laurent Bienvenu & Christopher P. Porter - 2016 - Bulletin of Symbolic Logic 22 (2):249-286.
Defining a randomness notion via another.Kojiro Higuchi & Ningning Peng - 2014 - Mathematical Logic Quarterly 60 (4-5):280-288.

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References found in this work

Computability and Randomness.André Nies - 2008 - Oxford, England: Oxford University Press UK.
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.
Randomness, Lowness and Degrees.George Barmpalias, Andrew E. M. Lewis & Mariya Soskova - 2008 - Journal of Symbolic Logic 73 (2):559 - 577.
Lowness for Kurtz randomness.Noam Greenberg & Joseph S. Miller - 2009 - Journal of Symbolic Logic 74 (2):665-678.

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