Abstract

ATuringdegreea is said to be almost everywhere dominating if, for almost all X ∈ 2 ω with respect to the “fair coin ” probability measure on 2 ω,andforallg: ω → ω Turing reducible to X, thereexistsf: 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. 1

Citations