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Remarks on the structure of tt-degrees based on constructive measure theory. (English) Zbl 0646.03039
Based on some results in constructive measure theory, classes of sets of natural numbers being of some interest from the point of view of both constructive mathematics and recursion theory are introduced and possibility of mutual tt-reducibility of their members is studied and, moreover, an arithmetization of the Lebesgue measurability of sets of reals is proposed.

03D30 Other degrees and reducibilities in computability and recursion theory
28A05 Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets
03F65 Other constructive mathematics
03D25 Recursively (computably) enumerable sets and degrees
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