Journal of Symbolic Logic 75 (1):387-400 (2010)

Abstract
We prove a number of results in effective randomness, using methods in which Π⁰₁ classes play an essential role. The results proved include the fact that every PA Turing degree is the join of two random Turing degrees, and the existence of a minimal pair of LR degrees below the LR degree of the halting problem.
Keywords Π⁰₁ classes   Martin-Löf randomness   Peano Arithmetic   K-trivials   Turing degrees   LR degrees
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DOI 10.2178/jsl/1264433928
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References found in this work BETA

Classical Recursion Theory.Peter G. Hinman - 2001 - Bulletin of Symbolic Logic 7 (1):71-73.
Calibrating Randomness.Rod Downey, Denis R. Hirschfeldt, André Nies & Sebastiaan A. Terwijn - 2006 - Bulletin of Symbolic Logic 12 (3):411-491.
Almost Everywhere Domination and Superhighness.Stephen G. Simpson - 2007 - Mathematical Logic Quarterly 53 (4):462-482.
Mass Problems and Hyperarithmeticity.Joshua A. Cole & Stephen G. Simpson - 2007 - Journal of Mathematical Logic 7 (2):125-143.

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Citations of this work BETA

A Hierarchy of Computably Enumerable Degrees.Rod Downey & Noam Greenberg - 2018 - Bulletin of Symbolic Logic 24 (1):53-89.
Low Upper Bounds in the LR Degrees.David Diamondstone - 2012 - Annals of Pure and Applied Logic 163 (3):314-320.
Algorithmic Randomness and Measures of Complexity.George Barmpalias - 2013 - Bulletin of Symbolic Logic 19 (3):318-350.

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