Journal of Symbolic Logic 77 (1):133-158 (2012)

Abstract
We show that every splitting of ${0}_{\mathrm{e}}^{\prime }$ in the local structure of the enumeration degrees, $$\mathcal{G}_{e} , contains at least one low-cuppable member. We apply this new structural property to show that the classes of all $\mathcal{K}$ -pairs in $\mathcal{G}_{e}$ , all downwards properly ${\mathrm{\Sigma }}_{2}^{0}$ enumeration degrees and all upwards properly ${\mathrm{\Sigma }}_{2}^{0}$ enumeration degrees are first order definable in $\mathcal{G}_{e}$
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DOI 10.2178/jsl/1327068696
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References found in this work BETA

Then-Rea Enumeration Degrees Are Dense.Alistair H. Lachlan & Richard A. Shore - 1992 - Archive for Mathematical Logic 31 (4):277-285.
Reducibility and Completeness for Sets of Integers.Richard M. Friedberg & Hartley Rogers - 1959 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 5 (7-13):117-125.
Definability of the Jump Operator in the Enumeration Degrees.I. Sh Kalimullin - 2003 - Journal of Mathematical Logic 3 (02):257-267.
Reducibility and Completeness for Sets of Integers.Richard M. Friedberg & Hartley Rogers - 1959 - Mathematical Logic Quarterly 5 (7‐13):117-125.

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Citations of this work BETA

The Automorphism Group of the Enumeration Degrees.Mariya I. Soskova - 2016 - Annals of Pure and Applied Logic 167 (10):982-999.

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