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Almost everywhere domination

Published online by Cambridge University Press:  12 March 2014

Natasha L. Dobrinen  and
Stephen G. Simpson
Natasha L. Dobrinen
Affiliation:
Department of Mathematics, Pennsylvania State University, 413 McAllister Bld, University Park, State College, PA 16802, USA, E-mail: [email protected], URL: http://www.math.psu.edu/dobrinen/
Stephen G. Simpson
Affiliation:
Department of Mathematics, Pennsylvania State University, 413 McAllister Bld, University Park, State College, PA 16802, USA, E-mail: [email protected], URL: http://www.math.psu.edu/simpson/
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Abstract.

A Turing degree a is said to be almost everywhere dominating if, for almost all X ∈ 2ω with respect to the “fair coin” probability measure on 2ω, and for all g: ω → ω Turing reducible to X, there exists f: ω → ω 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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 69 , Issue 3 , September 2004 , pp. 914 - 922
Copyright
Copyright © Association for Symbolic Logic 2004

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References

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