Geodesic
Simple Proofs of Some Theorems on High Degrees of Unsolvability
Canadian journal of mathematics, Tome 29 (1977) no. 5, pp. 1072-1080

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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. 
JR., Carl G. Jockusch. Simple Proofs of Some Theorems on High Degrees of Unsolvability. Canadian journal of mathematics, Tome 29 (1977) no. 5, pp. 1072-1080. doi: 10.4153/CJM-1977-105-5
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