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The Π3-theory of the -enumeration degrees is undecidable

Published online by Cambridge University Press:  12 March 2014

Thomas F. Kent
Thomas F. Kent*
Affiliation:
Department of Mathematics, Brigham Young University, Provo, UT 84602., USA, E-mail: kent@math.byu.edu
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Abstract

We show that in the language of { ≤ }. the Π3-fragment of the first order theory of the -enumeration degrees is undecidable. We then extend this result to show that the Π3-theory of any substructure of the enumeration degrees which contains the -degrees is undecidable.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 71 , Issue 4 , December 2006 , pp. 1284 - 1302
Copyright
Copyright © Association for Symbolic Logic 2006

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References

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