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Transactions of the American Mathematical Society

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Les modèles dénombrables d’une théorie ayant des fonctions de Skolem

Author: Daniel Lascar
Journal: Trans. Amer. Math. Soc. 268 (1981), 345-366
MSC: Primary 03C15; Secondary 03C45
MathSciNet review: 632533
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Abstract: Let $T$ be a countable complete theory having Skolem functions. We prove that if all the types over finitely generated models are definable (this is the case for example if $T$ is stable), then either $T$ has ${2^{{\aleph _0}}}$ countable models or all its models are homogeneous. The proof makes heavy use of stability techniques.

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Article copyright: © Copyright 1981 American Mathematical Society