Degree spectra of prime models

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

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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DOI http://projecteuclid.org/euclid.jsl/1082418536
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References found in this work BETA

Foundations of Recursive Model Theory.Terrence S. Millar - 1978 - Annals of Pure and Applied Logic 13 (1):45.
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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Citations of this work BETA

Computability of Homogeneous Models.Karen Lange & Robert I. Soare - 2007 - Notre Dame Journal of Formal Logic 48 (1):143-170.

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