Journal of Symbolic Logic

Bounding homogeneous models

Barbara F. Csima, Valentina S. Harizanov, Denis R. Hirschfeldt, and Robert I. Soare

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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.

Article information

Source
J. Symbolic Logic Volume 72, Issue 1 (2007), 305-323.

Dates
First available in Project Euclid: 23 March 2007

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

Citation

Csima, Barbara F.; Harizanov, Valentina S.; Hirschfeldt, Denis R.; Soare, Robert I. Bounding homogeneous models. Journal of Symbolic Logic 72 (2007), no. 1, 305--323. doi:10.2178/jsl/1174668397. http://projecteuclid.org/euclid.jsl/1174668397.


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