Subclasses of the Weakly Random Reals

Notre Dame Journal of Formal Logic 51 (4):417-426 (2010)
Abstract
The weakly random reals contain not only the Schnorr random reals as a subclass but also the weakly 1-generic reals and therefore the n -generic reals for every n . While the class of Schnorr random reals does not overlap with any of these classes of generic reals, their degrees may. In this paper, we describe the extent to which this is possible for the Turing, weak truth-table, and truth-table degrees and then extend our analysis to the Schnorr random and hyperimmune reals
Keywords weak randomness   Kurtz randomness   Schnorr randomness   recursive randomness   genericity   hyperimmune
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DOI 10.1215/00294527-2010-026
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