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March 2012 Cupping and definability in the local structure of the enumeration degrees
Hristo Ganchev, Mariya I. Soskova
J. Symbolic Logic 77(1): 133-158 (March 2012). DOI: 10.2178/jsl/1327068696

Abstract

We show that every splitting of 0e' in the local structure of the enumeration degrees, 𝔊e, contains at least one low-cuppable member. We apply this new structural property to show that the classes of all 𝓚-pairs in 𝔊e, all downwards properly Σ⁰₂ enumeration degrees and all upwards properly Σ⁰₂ enumeration degrees are first order definable in 𝔊e.

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Hristo Ganchev. Mariya I. Soskova. "Cupping and definability in the local structure of the enumeration degrees." J. Symbolic Logic 77 (1) 133 - 158, March 2012. https://doi.org/10.2178/jsl/1327068696

Information

Published: March 2012
First available in Project Euclid: 20 January 2012

zbMATH: 1241.03051
MathSciNet: MR2951634
Digital Object Identifier: 10.2178/jsl/1327068696

Rights: Copyright © 2012 Association for Symbolic Logic

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Vol.77 • No. 1 • March 2012
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