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- W2317058266 abstract "If a is a degree of unsolvability, a is called high if a ≦ 0’ and a’ = 0” . In [ 1 ], S. B. Cooper showed that if a is high, then (i) a is not a minimal degree, and (ii) there is a minimal degree b < a . We give new proofs of these results which avoid the intricate priority and recursive approximation arguments of [ 1 ] in favor of “oracle” constructions using the recursion theorem. Also our constructions apply to degrees a which are not below 0'. Call a degree a generalized high if a ’ = ( a U 0' )' . Among the degrees ≦ 0' , the generalized high degrees obviously coincide with the high degrees." @default.
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- W2317058266 date "1977-10-01" @default.
- W2317058266 modified "2023-09-25" @default.
- W2317058266 title "Simple Proofs of Some Theorems on High Degrees of Unsolvability" @default.
- W2317058266 doi "https://doi.org/10.4153/cjm-1977-105-5" @default.
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