Journal of Symbolic Logic

The Π₃-theory of the Σ⁰₂-enumeration degrees is undecidable

Thomas F. Kent

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Abstract

We show that in the language of {≤}, the Π₃-fragment of the first order theory of the Σ⁰₂-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 Δ⁰₂-degrees is undecidable.

Article information

Source
J. Symbolic Logic, Volume 71, Issue 4 (2006), 1284-1302.

Dates
First available in Project Euclid: 20 November 2006

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1164060455

Digital Object Identifier
doi:10.2178/jsl/1164060455

Mathematical Reviews number (MathSciNet)
MR2275859

Zentralblatt MATH identifier
1109.03036

Citation

Kent, Thomas F. The Π₃-theory of the Σ⁰₂-enumeration degrees is undecidable. J. Symbolic Logic 71 (2006), no. 4, 1284--1302. doi:10.2178/jsl/1164060455. https://projecteuclid.org/euclid.jsl/1164060455


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