Subclasses of the Weakly Random Reals
Johanna N. Y. Franklin
Source: Notre Dame J. Formal Logic Volume 51, Number 4
(2010), 417-426.
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.
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03D32
Keywords: weak randomness; Kurtz randomness; Schnorr randomness; recursive randomness; genericity; hyperimmune
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1285765796
Digital Object Identifier: doi:10.1215/00294527-2010-026
Zentralblatt MATH identifier: 05822354
Mathematical Reviews number (MathSciNet): MR2741834
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