Cupping and Jump Classes in the Computably Enumerable Degrees

Journal of Symbolic Logic 85 (4):1499-1545 (2020)
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Abstract

We show that there is a cuppable c.e. degree, all of whose cupping partners are high. In particular, not all cuppable degrees are${\operatorname {\mathrm {low}}}_3$-cuppable, or indeed${\operatorname {\mathrm {low}}}_n$cuppable for anyn, refuting a conjecture by Li. On the other hand, we show that one cannot improve highness to superhighness. We also show that the${\operatorname {\mathrm {low}}}_2$-cuppable degrees coincide with the array computable-cuppable degrees, giving a full understanding of the latter class.

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The continuity of cupping to 0'.Klaus Ambos-Spies, Alistair H. Lachlan & Robert I. Soare - 1993 - Annals of Pure and Applied Logic 64 (3):195-209.

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