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2014•Journal of Symbolic LogicRequires access

DECIDABLE MODELS OF ω-STABLE THEORIES

Uri Andrews

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Abstract

Abstract We characterize the ω-stable theories all of whose countable models admit decidable presentations. In particular, we show that for a countable ω-stable T, every countable model of T admits a decidable presentation if and only if all n-types in T are recursive and T has only countably many countable models. We further characterize the decidable models of ω-stable theories with countably many countable models as those which realize only recursive types.

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What this paper is about

Abstract We characterize the ω-stable theories all of whose countable models admit decidable presentations. In particular, we show that for a countable ω-stable T, every countable model of T admits a decidable presentation if and only if all n-types in T are recursive and T has only countably many countable models. We further characterize the decidable models of ω-stable theories with countably many countable models as those which realize only recursive types.

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Available abstract

Abstract We characterize the ω-stable theories all of whose countable models admit decidable presentations. In particular, we show that for a countable ω-stable T, every countable model of T admits a decidable presentation if and only if all n-types in T are recursive and T has only countably many countable models. We further characterize the decidable models of ω-stable theories with countably many countable models as those which realize only recursive types.

Key concepts: Countable set, Decidability, Mathematics, Discrete mathematics, Combinatorics

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