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The importance of Π1 0 classes in effective randomness

Published online by Cambridge University Press:  12 March 2014

George Barmpalias ,
Andrew E.M. Lewis  and
Keng Meng Ng
George Barmpalias
Affiliation:
School of Mathematics, Statistics, and Computer Science, Victoria University, Po Box 600 Wellington, New Zealand, E-mail: [email protected], URL: http.//www.mcs.vuw.ac.nz/~georgeb/
Andrew E.M. Lewis
Affiliation:
School of Mathematics, University of Leeds, Leeds LS2 9JT, UK, E-mail: [email protected], URL: http://www.aemlewis.co.uk
Keng Meng Ng
Affiliation:
School of Mathematics, Statistics, and Computer Science, Victoria University, Po Box 600 Wellington, New Zealand, E-mail: [email protected], URL: http://www.mcs.vuw.ac.nz/~selwyn/
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Abstract

We prove a number of results in effective randomness, using methods in which Π1 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

Π1 0 classesMartin-Löf randomnessPeano ArithmeticK-trivialsTuring degreesLR degrees
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 75 , Issue 1 , March 2010 , pp. 387 - 400
Copyright
Copyright © Association for Symbolic Logic 2010

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