Journal of Symbolic Logic

The importance of Π⁰₁ classes in effective randomness

George Barmpalias, Andrew E.M. Lewis, and Keng Meng Ng

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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.

Article information

Source
J. Symbolic Logic, Volume 75, Issue 1 (2010), 387-400.

Dates
First available in Project Euclid: 25 January 2010

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1264433928

Digital Object Identifier
doi:10.2178/jsl/1264433928

Mathematical Reviews number (MathSciNet)
MR2605901

Zentralblatt MATH identifier
1184.03039

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

Citation

Barmpalias, George; Lewis, Andrew E.M.; Ng, Keng Meng. The importance of Π⁰₁ classes in effective randomness. J. Symbolic Logic 75 (2010), no. 1, 387--400. doi:10.2178/jsl/1264433928. https://projecteuclid.org/euclid.jsl/1264433928


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