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September 2013 Low level nondefinability results: Domination and recursive enumeration
Mingzhong Cai, Richard A. Shore
J. Symbolic Logic 78(3): 1005-1024 (September 2013). DOI: 10.2178/jsl.7803180

Abstract

We study low level nondefinability in the Turing degrees. We prove a variety of results, including, for example, that being array nonrecursive is not definable by a $\Sigma_{1}$ or $\Pi_{1}$ formula in the language $(\leq ,\REA)$ where $\REA$ stands for the ``r.e.\ in and above'' predicate. In contrast, this property is definable by a $\Pi_{2}$ formula in this language. We also show that the $\Sigma_{1}$-theory of $(\mathcal{D},\leq ,\REA)$ is decidable.

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Mingzhong Cai. Richard A. Shore. "Low level nondefinability results: Domination and recursive enumeration." J. Symbolic Logic 78 (3) 1005 - 1024, September 2013. https://doi.org/10.2178/jsl.7803180

Information

Published: September 2013
First available in Project Euclid: 6 January 2014

zbMATH: 1325.03047
MathSciNet: MR3135511
Digital Object Identifier: 10.2178/jsl.7803180

Subjects:
Primary: 03D28

Rights: Copyright © 2013 Association for Symbolic Logic

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Vol.78 • No. 3 • September 2013
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