Abstract
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 < x ≤ a, there is a low n c. e. degree y such that x ∨ y = 0′.
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Wang, S., Wu, G. (2011). On a Hierarchy of Plus-Cupping Degrees. In: Löwe, B., Normann, D., Soskov, I., Soskova, A. (eds) Models of Computation in Context. CiE 2011. Lecture Notes in Computer Science, vol 6735. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21875-0_33
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DOI: https://doi.org/10.1007/978-3-642-21875-0_33
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