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Low Level Nondelegability Results: Domination and Recursive Enumeration

Published online by Cambridge University Press:  12 March 2014

Mingzhong Cai  and
Richard A. Shore
Mingzhong Cai
Affiliation:
Department of Mathematics, University of Wisconsin, Madison WI 53705, USA, E-Mail: mcai@math.wisc.edu
Richard A. Shore
Affiliation:
Department of Mathematics, Cornell University, Ithaca NY 14853, USA, E-mail: shore@math.cornell.edu
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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 Σ1 or Π1 formula in the language (≤, REA) where REA stands for the “r.e. in and above” predicate. In contrast, this property is definable by a Π2 formula in this language. We also show that the Σ1-theory of (, ≤, REA) is decidable.

Keywords

03D28
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 78 , Issue 3 , September 2013 , pp. 1005 - 1024
Copyright
Copyright © Association for Symbolic Logic 2013

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References

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