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The importance of Π⁰₁ classes in effective randomness
George Barmpalias, Andrew E.M. Lewis, and Keng Meng Ng
Source: J. Symbolic Logic Volume 75, Issue 1
(2010), 387-400.
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.
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Keywords: Π⁰₁ classes; Martin-Löf randomness; Peano Arithmetic; K-trivials; Turing degrees; LR degrees
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jsl/1264433928
Digital Object Identifier: doi:10.2178/jsl/1264433928
Zentralblatt MATH identifier: 05681311
Mathematical Reviews number (MathSciNet): MR2605901
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