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A new proof of Friedman’s conjecture. (English) Zbl 1242.03064
In [“One hundred and two problems in mathematical logic”, J. Symb. Log. 40, 113–129 (1975; Zbl 0318.02002)], H. Friedman conjectured that every uncountable \(\Delta_1^1\) set of reals has a member of each hyperdegree greater than or equal to the hyperdegree of Kleene’s \(\vartheta\). Eventually the conjecture was confirmed by D. A. Martin [“Proof of a conjecture of Friedman”, Proc. Am. Math. Soc. 55, 129 (1976; Zbl 0325.02029)] and, independently, by Friedman himself. In this paper the author gives a new proof of Friedman’s conjecture.

MSC:
03D30 Other degrees and reducibilities in computability and recursion theory
03D25 Recursively (computably) enumerable sets and degrees
Keywords:
hyperdegree; reals
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References:
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[2] DOI: 10.2307/2271891 · Zbl 0318.02002
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