Israel Journal of Mathematics

, Volume 49, Issue 1–3, pp 259–280 | Cite as

A proof of vaught’s conjecture forω-stable theories

  • S. Shelah
  • L. Harrington
  • M. Makkai


In this paper it is proved that ifT is a countable completeω-stable theory in ordinary logic, thenT has either continuum many, or at most countably many, non-isomorphic countable models.


Prime Model Finite Subset Countable Model ellA Isomorphic Copy 
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  1. 1.
    M. M. Makkai,A survey of basic stability theory, with particular emphasis on orthogonality and regular types, Isr. J. Math.49 (1984), 181–238 (this issue).zbMATHMathSciNetGoogle Scholar
  2. 2.
    H-M. L. Harrington and M. Makkai,An exposition of Shelah’s ‘Main Gap’: counting uncountable models of ω-stable and superstable theories, Notre Dame J. Formal Logic, to appear.Google Scholar
  3. 3.
    D. Lascar,Les modèles dénombrables d’une théorie ayant des fonctions de Skolem, Trans. Am. Math. Soc.268 (1981), 345–366.zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    E. Bouscaren and D. Lascar,Countable models of non-multidimensional0-stable theories, J. Symb. Logic48 (1983), 197–205.zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    E. Bouscaren,Countable models of multidimensional0-stable theories, J. Symb. Logic48 (1983), 377–383.zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    M. Morley,The number of countable models, J. Symb. Logic35 (1970), 14–18.zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    J. Saffe,On Vaught’s conjecture for superstable theories, to appear.Google Scholar
  8. 8.
    J. Saffe,Einige Ergebnisse uber die Auzahl abrahlbarer Modelle superstabiler Theorien, Dissertation, Universitat Hannover, 1981.Google Scholar

Copyright information

© Hebrew University 1984

Authors and Affiliations

  • S. Shelah
    • 1
  • L. Harrington
    • 1
  • M. Makkai
    • 1
  1. 1.Institute for Advanced StudiesThe Hebrew University of JerusalemJerusalemIsrael

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