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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.


References [Enhancements On Off] (What's this?)

  • [L1] Daniel Lascar, Sur les théorie convexes “modèles complètes”, C. R. Acad. Sci. Paris Sér. A 278 (1974), 1001–1004 (French). MR 0349376
  • [L2] -, Généralisation de l'ordre de Rudin-Keisler aux types d'une theorie, Colloq. Internat. C.N.R.S., No. 249, Clermont-Ferrand, 1975, pp. 73-81.
  • [L3] -, Les modèles dénombrables d'une théorie superstable ayant des fonctions de Skolem, C. R. Acad. Sci. Paris Sér. A 289 (1979), 655-658.
  • [LP] Daniel Lascar and Bruno Poizat, An introduction to forking, J. Symbolic Logic 44 (1979), no. 3, 330–350. MR 540665, 10.2307/2273127
  • [S1] Saharon Shelah, Classification theory and the number of nonisomorphic models, Studies in Logic and the Foundations of Mathematics, vol. 92, North-Holland Publishing Co., Amsterdam-New York, 1978. MR 513226
  • [S2] Saharon Shelah, End extensions and numbers of countable models, J. Symbolic Logic 43 (1978), no. 3, 550–562. MR 503792, 10.2307/2273531
  • [V] R. L. Vaught, Denumerable models of complete theories, Infinitistic Methods (Proc. Sympos. Foundations of Math., Warsaw, 1959), Pergamon, Oxford; Państwowe Wydawnictwo Naukowe, Warsaw, 1961, pp. 303–321. MR 0186552

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DOI: https://doi.org/10.1090/S0002-9947-1981-0632533-X
Article copyright: © Copyright 1981 American Mathematical Society