Pi0a Classes and Minimal Degrees
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Abstract Theorem. There is a non-empty Π10 class of reals, each of which computes a real of minimal (Turing) degree. Corollary. WKL ⊢ “there is a minimal Turing degree”. This answers a question of H. Friedman and S. Simpson.
[1] C. E. M. Yates,et al. Initial segments of the degrees of unsolvability Part II: minimal degrees , 1970, Journal of Symbolic Logic.
[2] G. Sacks. A minimal degree less than 0 , 1961 .