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Bounding homogenous models

  • Barbara F. Csima (a1), Valentina S. Harizanov (a2), Denis R. Hirschfeldt (a3) and Robert I. Soare (a4)

Abstract

A Turing degree d is homogeneous bounding if every complete decidable (CD) theory has a d-decidable homogeneous model , i.e., the elementary diagram De () 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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Bounding homogenous models

  • Barbara F. Csima (a1), Valentina S. Harizanov (a2), Denis R. Hirschfeldt (a3) and Robert I. Soare (a4)

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