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June 2010 Interpreting true arithmetic in the Δ02-enumeration degrees
Thomas F. Kent
J. Symbolic Logic 75(2): 522-550 (June 2010). DOI: 10.2178/jsl/1268917493

Abstract

We show that there is a first order sentence φ(x; a, b, l) such that for every computable partial order 𝒫 and Δ02-degree u > 0e, there are Δ02-enumeration degrees au, b, and l such that 𝒫 ≅ {x : φ(x; a, b, l)}. Allowing 𝒫 to be a suitably defined standard model of arithmetic gives a parameterized interpretation of true arithmetic in the Δ02-enumeration degrees. Finally we show that there is a first order sentence that correctly identifies a subset of the standard models, which gives a parameterless interpretation of true arithmetic in the Δ02-enumeration degrees.

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Thomas F. Kent. "Interpreting true arithmetic in the Δ02-enumeration degrees." J. Symbolic Logic 75 (2) 522 - 550, June 2010. https://doi.org/10.2178/jsl/1268917493

Information

Published: June 2010
First available in Project Euclid: 18 March 2010

zbMATH: 1192.03019
MathSciNet: MR2648154
Digital Object Identifier: 10.2178/jsl/1268917493

Rights: Copyright © 2010 Association for Symbolic Logic

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Vol.75 • No. 2 • June 2010
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