The importance of Π⁰₁ classes in effective randomness

Journal of Symbolic Logic 75 (1):387-400 (2010)
Abstract
We prove a number of results in effective randomness, using methods in which $\Pi _{1}^{0}$ 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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Low Upper Bounds in the LR Degrees.David Diamondstone - 2012 - Annals of Pure and Applied Logic 163 (3):314-320.

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