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- W2022731330 abstract "Let denote the set of degrees ≤ 0 ′. A degree a ≤ 0 ′ is said to be complemented in if there exists a degree b ≤ 0 ′ such that b ∪ a = 0 ′ and b ∩ a = 0 . R.W. Robinson (cf. [11]) showed that every degree a ≤ 0 ′ satisfying a ″ = 0 ″ is complemented in and the author [8] showed that every degree a ≤ 0 ′ satisfying a ′ = 0 ″ is complemented in . Also, in [2], R. L. Epstein showed that every r.e. degree is complemented in . In this paper we will show that in fact every degree ≤ 0 ′ is complemented in . We will further show that the same is true in the upper semilattice of degrees ≤ c , where c is any complete degree. This is in contrast to the situation in the upper semilattice of r.e. degrees in which, as Lachlan [6] has shown, no degree other than 0 and 0 ′ is complemented." @default.
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- W2022731330 date "1981-12-01" @default.
- W2022731330 modified "2023-09-26" @default.
- W2022731330 title "The upper semilattice of degrees ≤ 0′ is complemented " @default.
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- W2022731330 doi "https://doi.org/10.2307/2273220" @default.
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