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The importance of Π10 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: George.Barmpalias@mcs.vuw.ac.nz, 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: andy@aemlewis.co.uk, 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: keng.meng.ng@mcs.vuw.ac.nz, 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 Π10 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

Π10 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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