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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
##### Citations:
Zbl 0318.02002; Zbl 0325.02029
Full Text:
##### References:
 [1] DOI: 10.2307/2273508 · Zbl 0398.03039 [2] DOI: 10.2307/2271891 · Zbl 0318.02002 [3] DOI: 10.1007/s11856-008-1019-9 · Zbl 1153.03020 [4] DOI: 10.1090/S0002-9947-1975-0392534-3 [5] DOI: 10.1112/jlms/jdm022 · Zbl 1118.03034 [6] Higher recursion theory (1990) · Zbl 0716.03043 [7] Studies in Logic and the Foundations of Mathematics 100 (1980) [8] DOI: 10.1090/S0002-9939-1976-0406785-9 [9] Cabal seminar 79–81 1019 pp 199– (1983) [10] Oxford Logic Guides 51 (2009)
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