Almost everywhere domination

Journal of Symbolic Logic 69 (3):914-922 (2004)
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Abstract

A Turing degree a is said to be almost everywhere dominating if, for almost all $X \in 2^{\omega}$ with respect to the "fair coin" probability measure on $2^{\omega}$ , and for all g: $\omega \rightarrow \omega$ Turing reducible to X, there exists f: $\omega \rightarrow \omega$ of Turing degree a which dominates g. We study the problem of characterizing the almost everywhere dominating Turing degrees and other, similarly defined classes of Turing degrees. We relate this problem to some questions in the reverse mathematics of measure theory

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Citations of this work

Almost everywhere domination and superhighness.Stephen G. Simpson - 2007 - Mathematical Logic Quarterly 53 (4):462-482.
A survey of Mučnik and Medvedev degrees.Peter G. Hinman - 2012 - Bulletin of Symbolic Logic 18 (2):161-229.
Denjoy, Demuth and density.Laurent Bienvenu, Rupert Hölzl, Joseph S. Miller & André Nies - 2014 - Journal of Mathematical Logic 14 (1):1450004.
Mass problems and almost everywhere domination.Stephen G. Simpson - 2007 - Mathematical Logic Quarterly 53 (4):483-492.
Tracing and domination in the Turing degrees.George Barmpalias - 2012 - Annals of Pure and Applied Logic 163 (5):500-505.

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References found in this work

Measure theory and weak König's lemma.Xiaokang Yu & Stephen G. Simpson - 1990 - Archive for Mathematical Logic 30 (3):171-180.
N? Sets and models of wkl0.Stephen G. Simpson - 2005 - In Stephen Simpson (ed.), Reverse Mathematics 2001. pp. 21--352.
Vitali's Theorem and WWKL.Douglas K. Brown, Mariagnese Giusto & Stephen G. Simpson - 2002 - Archive for Mathematical Logic 41 (2):191-206.
Lebesgue Convergence Theorems and Reverse Mathematics.Xiaokang Yu - 1994 - Mathematical Logic Quarterly 40 (1):1-13.

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