The limitations of cupping in the local structure of the enumeration degrees

Archive for Mathematical Logic 49 (2):169-193 (2010)
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Abstract

We prove that a sequence of sets containing representatives of cupping partners for every nonzero ${\Delta^0_2}$ enumeration degree cannot have a ${\Delta^0_2}$ enumeration. We also prove that no subclass of the ${\Sigma^0_2}$ enumeration degrees containing the nonzero 3-c.e. enumeration degrees can be cupped to ${\mathbf{0}_e'}$ by a single incomplete ${\Sigma^0_2}$ enumeration degree

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Citations of this work

Avoiding uniformity in the Δ 2 0 enumeration degrees.Liliana Badillo & Charles M. Harris - 2014 - Annals of Pure and Applied Logic 165 (9):1355-1379.

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References found in this work

Computability Theory.S. Barry Cooper - 2003 - Chapman & Hall.
Then-rea enumeration degrees are dense.Alistair H. Lachlan & Richard A. Shore - 1992 - Archive for Mathematical Logic 31 (4):277-285.
Finite cupping sets.Andrew Lewis - 2004 - Archive for Mathematical Logic 43 (7):845-858.

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