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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



On the degree spectrum of a $ \Pi^0_1$ class

Authors: Thomas Kent and Andrew E. M. Lewis
Journal: Trans. Amer. Math. Soc. 362 (2010), 5283-5319
MSC (2010): Primary 03D28
Published electronically: May 4, 2010
MathSciNet review: 2657680
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Abstract: For any $ \mathcal{P} \subseteq 2^{\omega} $, define $ S(\mathcal{P}) $, the degree spectrum of $ \mathcal{P}$, to be the set of all Turing degrees $ \bf {a} $ such that there exists $ A\in \mathcal{P} $ of degree $ \bf {a} $. We prove a number of basic properties of the structure which is the degree spectra of $ \Pi^0_1$ classes ordered by inclusion and also study in detail some other phenomena relating to the study of $ \Pi^0_1$ classes from a degree theoretic point of view, which are brought to light as a result of this analysis.

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Additional Information

Thomas Kent
Affiliation: Department of Mathematics, Marywood University, Scranton, Pennsylvania 18509

Andrew E. M. Lewis
Affiliation: Department of Mathematics, University of Leeds, Leeds, England LS2 9JT

Keywords: $\Pi ^0_1$ classes
Received by editor(s): June 13, 2008
Published electronically: May 4, 2010
Additional Notes: The first author was supported by Marie-Curie Fellowship MIFI-CT-2006-021702.
The second author was supported by a Royal Society University Research Fellowship.
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.