Recursively enumerable sets and degrees
Recursively enumerable sets and degrees
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Greenberg, Ng and Wu proved in a recent paper the existence of a cuppable degree a that can be cupped to 0′ by high degrees only. A corollary of this result shows that such a degree a can be high, and hence bounds noncuppable degrees. In this paper, we prove the existence of a plus-cupping degree which can only be cupped to 0′by high degrees. This refutes Li-Wang's claim that every plus-cupping degree is 3-plus-cupping, where a nonzero c. e. degree a is n-plus-cupping if for every c. e. degree x with 0 n c. e. degree y such that x ∨ y = 0′.