Journal of Symbolic Logic

Promptness does not imply superlow cuppability

David Diamondstone

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A classical theorem in computability is that every promptly simple set can be cupped in the Turing degrees to some complete set by a low c.e. set. A related question due to A. Nies is whether every promptly simple set can be cupped by a superlow c.e. set, i.e. one whose Turing jump is truth-table reducible to the halting problem ∅'. A negative answer to this question is provided by giving an explicit construction of a promptly simple set that is not superlow cuppable. This problem relates to effective randomness and various lowness notions.

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J. Symbolic Logic, Volume 74, Issue 4 (2009), 1264-1272.

First available in Project Euclid: 5 October 2009

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Diamondstone, David. Promptness does not imply superlow cuppability. J. Symbolic Logic 74 (2009), no. 4, 1264--1272. doi:10.2178/jsl/1254748690.

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