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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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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DOI: http://dx.doi.org/10.1090/S0002-9947-1981-0632533-X
PII: S 0002-9947(1981)0632533-X
Article copyright: © Copyright 1981 American Mathematical Society