Bounding Homogeneous Models

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

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Valentina Harizanov
George Washington University

Citations of this work

The degree spectra of homogeneous models.Karen Lange - 2008 - Journal of Symbolic Logic 73 (3):1009-1028.
Computability of Homogeneous Models.Karen Lange & Robert I. Soare - 2007 - Notre Dame Journal of Formal Logic 48 (1):143-170.

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References found in this work

Computable structures and the hyperarithmetical hierarchy.C. J. Ash - 2000 - New York: Elsevier. Edited by J. Knight.
Degrees coded in jumps of orderings.Julia F. Knight - 1986 - Journal of Symbolic Logic 51 (4):1034-1042.
Recursively presentable prime models.Leo Harrington - 1974 - Journal of Symbolic Logic 39 (2):305-309.
Bounding Prime Models.Barbara F. Csima, Denis R. Hirschfeldt, Julia F. Knight & Robert I. Soare - 2004 - Journal of Symbolic Logic 69 (4):1117 - 1142.

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