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December 2010 A high c.e. degree which is not the join of two minimal degrees
Matthew B. Giorgi
J. Symbolic Logic 75(4): 1339-1358 (December 2010). DOI: 10.2178/jsl/1286198150

Abstract

We construct a high c.e. degree which is not the join of two minimal degrees and so refute Posner's conjecture that every high c.e. degree is the join of two minimal degrees. Additionally, the proof shows that there is a high c.e. degree a such that for any splitting of a into degrees b and c one of these degrees bounds a 1-generic degree.

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Matthew B. Giorgi. "A high c.e. degree which is not the join of two minimal degrees." J. Symbolic Logic 75 (4) 1339 - 1358, December 2010. https://doi.org/10.2178/jsl/1286198150

Information

Published: December 2010
First available in Project Euclid: 4 October 2010

zbMATH: 1216.03055
MathSciNet: MR2767972
Digital Object Identifier: 10.2178/jsl/1286198150

Rights: Copyright © 2010 Association for Symbolic Logic

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Vol.75 • No. 4 • December 2010
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