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March 2010 The importance of Π⁰₁ classes in effective randomness
George Barmpalias, Andrew E.M. Lewis, Keng Meng Ng
J. Symbolic Logic 75(1): 387-400 (March 2010). DOI: 10.2178/jsl/1264433928

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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George Barmpalias. Andrew E.M. Lewis. Keng Meng Ng. "The importance of Π⁰₁ classes in effective randomness." J. Symbolic Logic 75 (1) 387 - 400, March 2010. https://doi.org/10.2178/jsl/1264433928

Information

Published: March 2010
First available in Project Euclid: 25 January 2010

zbMATH: 1184.03039
MathSciNet: MR2605901
Digital Object Identifier: 10.2178/jsl/1264433928

Keywords: K-trivials , LR degrees , Martin-Löf randomness , Peano Arithmetic , Turing degrees , Π⁰₁ classes

Rights: Copyright © 2010 Association for Symbolic Logic

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Vol.75 • No. 1 • March 2010
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