Notre Dame Journal of Formal Logic

Subclasses of the Weakly Random Reals

Johanna N. Y. Franklin


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.

Article information

Notre Dame J. Formal Logic, Volume 51, Number 4 (2010), 417-426.

First available in Project Euclid: 29 September 2010

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03D32: Algorithmic randomness and dimension [See also 68Q30]

weak randomness Kurtz randomness Schnorr randomness recursive randomness genericity hyperimmune


Franklin, Johanna N. Y. Subclasses of the Weakly Random Reals. Notre Dame J. Formal Logic 51 (2010), no. 4, 417--426. doi:10.1215/00294527-2010-026.

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