Degrees joining to 0' [Book Review]

Journal of Symbolic Logic 46 (4):714 - 722 (1981)
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Abstract

It is shown that if A and C are sets of degrees uniformly recursive in 0' with $\mathbf{0} \nonin \mathscr{C}$ then there is a degree b with b' = 0', b ∪ c = 0' for every c ∈ C, and $\mathbf{a} \nleq \mathbf{b}$ for every a ∈ A ∼ {0}. The proof is given as an oracle construction recursive in 0'. It follows that any nonrecursive degree below 0' can be joined to 0' by a degree strictly below 0'. Also, if $\mathbf{a ' and a" = 0" then there is a degree b such that a ∪ b = 0' and a ∩ b = 0

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References found in this work

The Degrees of Hyperimmune Sets.Webb Miller & D. A. Martin - 1968 - Mathematical Logic Quarterly 14 (7-12):159-166.
The Degrees of Hyperimmune Sets.Webb Miller & D. A. Martin - 1968 - Mathematical Logic Quarterly 14 (7‐12):159-166.
Degrees of Unsolvability.Leonard P. Sasso - 1975 - Journal of Symbolic Logic 40 (3):452-453.

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