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  1. Degrees of unsolvability: local and global theory.Manuel Lerman - 1983 - New York: Springer Verlag.
    I first seriously contemplated writing a book on degree theory in 1976 while I was visiting the University of Illinois at Chicago Circle. There was, at that time, some interest in ann-series book about degree theory, and through the encouragement of Bob Soare, I decided to make a proposal to write such a book. Degree theory had, at that time, matured to the point where the local structure results which had been the mainstay of the earlier papers in the area (...)
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  • (1 other version)Double Jumps of Minimal Degrees.Carl G. Jockusch & David B. Posner - 1978 - Journal of Symbolic Logic 43 (4):715 - 724.
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  • Direct and local definitions of the Turing jump.Richard A. Shore - 2007 - Journal of Mathematical Logic 7 (2):229-262.
    We show that there are Π5 formulas in the language of the Turing degrees, [Formula: see text], with ≤, ∨ and ∧, that define the relations x″ ≤ y″, x″ = y″ and so {x ∈ L2 = x ≥ y|x″ = y″} in any jump ideal containing 0. There are also Σ6&Π6 and Π8 formulas that define the relations w = x″ and w = x', respectively, in any such ideal [Formula: see text]. In the language with just ≤ (...)
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  • A minimal degree not realizing least possible jump.Leonard P. Sasso - 1974 - Journal of Symbolic Logic 39 (3):571-574.
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  • Bounding non- GL ₂ and R.E.A.Klaus Ambos-Spies, Decheng Ding, Wei Wang & Liang Yu - 2009 - Journal of Symbolic Logic 74 (3):989-1000.
    We prove that every Turing degree a bounding some non-GL₂ degree is recursively enumerable in and above (r.e.a.) some 1-generic degree.
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  • A Hyperimmune Minimal Degree and an ANR 2-Minimal Degree.Mingzhong Cai - 2010 - Notre Dame Journal of Formal Logic 51 (4):443-455.
    We develop a new method for constructing hyperimmune minimal degrees and construct an ANR degree which is a minimal cover of a minimal degree.
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