Bounding homogeneous models

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.

• Type: Journal
• Year: 2007
• Where: JSYML
• Authors: Barbara F. Csima, Valentina S. Harizanov, Denis R. Hirschfeldt, Robert I. Soare
• Keywords: D-decidable Homogeneous Model, Homogeneous Model, JSYML 2007, PA Degree