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On the jump classes of noncuppable enumeration degrees

Published online by Cambridge University Press:  12 March 2014

Charles M. Harris
Charles M. Harris*
Affiliation:
University of Leeds, Department of Mathematics, Leeds, UK, E-mail: [email protected], URL: http://www.maths.leeds.ac.uk/~charlie
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Abstract

We prove that for every Σ20 enumeration degree b there exists a noncuppable Σ20 degree a > 0e such that and . This allows us to deduce, from results on the high/low jump hierarchy in the local Turing degrees and the jump preserving properties of the standard embedding , that there exist Σ20 noncuppable enumeration degrees at every possible—i.e., above low1—level of the high/low jump hierarchy in the context of .

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 76 , Issue 1 , March 2011 , pp. 177 - 197
Copyright
Copyright © Association for Symbolic Logic 2011

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