A non-splitting theorem in the enumeration degrees

doi:10.1016/j.apal.2009.01.009

Annals of Pure and Applied Logic

Volume 160, Issue 3, September 2009, Pages 400-418

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Abstract

We complete a study of the splitting/non-splitting properties of the enumeration degrees below $0_{e}^{'}$ by proving an analog of Harrington’s non-splitting theorem for the $Σ_{2}^{0}$ enumeration degrees. We show how non-splitting techniques known from the study of the c.e. Turing degrees can be adapted to the enumeration degrees.

MSC

03D30

Keywords

Enumeration reducibility

Σ_{2}^{0}

e-degrees

Non-splitting

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^☆: The author is partially supported by Marie Curie Early Training Site MATHLOGAPS (MEST-CT-2004-504029) and by the National Science Fund of Bulgaria under project “Computability with Partial Information”.

Annals of Pure and Applied Logic

A non-splitting theorem in the enumeration degrees☆

Abstract

MSC

Keywords