DECIDABLE MODELS OF ω-STABLETHEORIES

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 model...

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Veröffentlicht in:	The Journal of symbolic logic 2014-03, Vol.79 (1), p.186-192
1. Verfasser:	Andrews, Uri
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Sprache:	eng
Schlagworte:	Logic Mathematics Philosophy Realism
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container_title	The Journal of symbolic logic
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creator	Andrews, Uri
description	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.
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source	JSTOR Mathematics & Statistics; JSTOR Archive Collection A-Z Listing; Cambridge University Press Journals Complete
subjects	Logic Mathematics Philosophy Realism
title	DECIDABLE MODELS OF ω-STABLETHEORIES
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