Degree Spectra of Prime Models

Journal of Symbolic Logic 69 (2):430 - 442 (2004)
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Abstract

We consider the Turing degrees of prime models of complete decidable theories. In particular we show that every complete decidable atomic theory has a prime model whose elementary diagram is low. We combine the construction used in the proof with other constructions to show that complete decidable atomic theories have low prime models with added properties. If we have a complete decidable atomic theory with all types of the theory computable, we show that for every degree d with 0 0, T has a d-decidable model omitting the nonprincipal types listed by L

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Citations of this work

A characterization of the 0 -basis homogeneous bounding degrees.Karen Lange - 2010 - Journal of Symbolic Logic 75 (3):971-995.
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

Foundations of recursive model theory.Terrence S. Millar - 1978 - Annals of Mathematical Logic 13 (1):45.

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