Bounding homogeneous models
Barbara F. Csima, Valentina S. Harizanov, Denis R. Hirschfeldt, and Robert I. Soare
Source: J. Symbolic Logic Volume 72, Issue 1
(2007), 305-323.
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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Permanent link to this document: http://projecteuclid.org/euclid.jsl/1174668397
Digital Object Identifier: doi:10.2178/jsl/1174668397
Mathematical Reviews number (MathSciNet): MR2298484
Zentralblatt MATH identifier: 1116.03027
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