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March 2007 Bounding homogeneous models
Barbara F. Csima, Valentina S. Harizanov, Denis R. Hirschfeldt, Robert I. Soare
J. Symbolic Logic 72(1): 305-323 (March 2007). DOI: 10.2178/jsl/1174668397

Abstract

A Turing degree d is homogeneous bounding if every complete decidable (CD) theory has a d-decidable homogeneous model 𝒜, i.e., the elementary diagram De(𝒜) has degree d. It follows from results of Macintyre and Marker that every PA degree (i.e., every degree of a complete extension of Peano Arithmetic) is homogeneous bounding. We prove that in fact a degree is homogeneous bounding if and only if it is a PA degree. We do this by showing that there is a single CD theory T such that every homogeneous model of T has a PA degree.

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Barbara F. Csima. Valentina S. Harizanov. Denis R. Hirschfeldt. Robert I. Soare. "Bounding homogeneous models." J. Symbolic Logic 72 (1) 305 - 323, March 2007. https://doi.org/10.2178/jsl/1174668397

Information

Published: March 2007
First available in Project Euclid: 23 March 2007

zbMATH: 1116.03027
MathSciNet: MR2298484
Digital Object Identifier: 10.2178/jsl/1174668397

Rights: Copyright © 2007 Association for Symbolic Logic

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Vol.72 • No. 1 • March 2007
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