Journal of Symbolic Logic

Almost everywhere domination

Natasha L. Dobrinen and Stephen G. Simpson

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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.

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J. Symbolic Logic, Volume 69, Issue 3 (2004), 914-922.

First available in Project Euclid: 4 October 2004

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Dobrinen, Natasha L.; Simpson, Stephen G. Almost everywhere domination. J. Symbolic Logic 69 (2004), no. 3, 914--922. doi:10.2178/jsl/1096901775.

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