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December 2011 Degree invariance in the Π01 classes
Rebecca Weber
J. Symbolic Logic 76(4): 1184-1210 (December 2011). DOI: 10.2178/jsl/1318338845

Abstract

Let ℰΠ denote the collection of all Π01 classes, ordered by inclusion. A collection of Turing degrees 𝒞 is called invariant over ℰΠ if there is some collection 𝒮 of Π01 classes representing exactly the degrees in 𝒞 such that 𝒮 is invariant under automorphisms of ℰΠ. Herein we expand the known degree invariant classes of ℰΠ, previously including only {0} and the array noncomputable degrees, to include all highn and non-lown degrees for n≥2. This is a corollary to a very general definability result. The result is carried out in a substructure G of ℰΠ, within which the techniques used model those used by Cholak and Harrington [6] to obtain the same definability for the c.e. sets. We work back and forth between G and ℰΠ to show that this definability in G gives the desired degree invariance over ℰΠ.

Citation

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Rebecca Weber. "Degree invariance in the Π01 classes." J. Symbolic Logic 76 (4) 1184 - 1210, December 2011. https://doi.org/10.2178/jsl/1318338845

Information

Published: December 2011
First available in Project Euclid: 11 October 2011

MathSciNet: MR2895392
Digital Object Identifier: 10.2178/jsl/1318338845

Subjects:
Primary: 03D25, 03D28

Rights: Copyright © 2011 Association for Symbolic Logic

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Vol.76 • No. 4 • December 2011
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