A measure-theoretic proof of Turing incomparability
The main result of this paper is that whenever \(A\) is a noncomputable set in an \(\omega\)-model of WWKL, there is another set \(B\) in the model which is Turing incomparable to \(A\). This theorem extends the similar result for \(\omega\)-models of WKL proved by \textit{A. Kučera} and \textit{T. A. Slaman} [``Turing incomparability in Scott sets'', Proc. Am. Math. Soc. 135, No. 11, 3723--3731 (2007; Zbl 1123.03039)], which answers a question of Friedman and McAllister; see [\textit{D. Cenzer} and \textit{C. G. Jockusch jun.}, ``\(\Pi^0_1\) classes -- structure and applications'', Contemp. Math. 257, 39--59 (2000; Zbl 0962.03040)]. The exposition includes a clear and concise discussion of genercity and randomness, relating these concepts to the main result.
scientific article; zbMATH DE number 5947122
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