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DECIDABLE MODELS OF ω-STABLETHEORIES

Published online by Cambridge University Press:  17 April 2014

URI ANDREWS
URI ANDREWS*
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF WISCONSIN, MADISON 480 LINCOLN DR., MADISON, WI 53706-1388, USA E-mail: andrews@math.wisc.edu
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Abstract

We characterize the ω-stable theories all of whosecountable models admit decidable presentations. In particular, we show that fora countable ω-stable T, everycountable model of T admits a decidable presentation if andonly if all n-types in T are recursive andT has only countably many countable models. We furthercharacterize the decidable models of ω-stabletheories with countably many countable models as those which realize onlyrecursive types.

Keywords

Decidable modelsstrongly constructivizable modelsω-stable

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Type
Articles
Information
The Journal of Symbolic Logic , Volume 79 , Issue 1 , March 2014 , pp. 186 - 192
Copyright
Copyright © Association for Symbolic Logic 2014 

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References

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