Almost everywhere domination
Copyright policy )Almost everywhere domination
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.
- Pennsylvania State University United States
Other connections with logic and set theory, Other Turing degree structures, Turing degrees, Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets, reverse mathematics, measure, Second- and higher-order arithmetic and fragments, Foundations of classical theories (including reverse mathematics), domination
Other connections with logic and set theory, Other Turing degree structures, Turing degrees, Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets, reverse mathematics, measure, Second- and higher-order arithmetic and fragments, Foundations of classical theories (including reverse mathematics), domination
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