Journal of Symbolic Logic 72 (1):305 - 323 (2007)

Valentina Harizanov
George Washington University
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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DOI 10.2178/jsl/1174668397
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References found in this work BETA

Degrees Coded in Jumps of Orderings.Julia F. Knight - 1986 - Journal of Symbolic Logic 51 (4):1034-1042.
Foundations of Recursive Model Theory.Terrence S. Millar - 1978 - Annals of Pure and Applied Logic 13 (1):45.
Recursively Presentable Prime Models.Leo Harrington - 1974 - Journal of Symbolic Logic 39 (2):305-309.

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The Degree Spectra of Homogeneous Models.Karen Lange - 2008 - Journal of Symbolic Logic 73 (3):1009-1028.

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