Skip to main content
SpringerLink
Log in

A proof of vaught’s conjecture forω-stable theories

  • Published:
Israel Journal of Mathematics Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  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).

    MATH  MathSciNet  Google Scholar 

  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.

  3. D. Lascar,Les modèles dénombrables d’une théorie ayant des fonctions de Skolem, Trans. Am. Math. Soc.268 (1981), 345–366.

    Article  MATH  MathSciNet  Google Scholar 

  4. E. Bouscaren and D. Lascar,Countable models of non-multidimensional ℵ0-stable theories, J. Symb. Logic48 (1983), 197–205.

    Article  MATH  MathSciNet  Google Scholar 

  5. E. Bouscaren,Countable models of multidimensional ℵ0-stable theories, J. Symb. Logic48 (1983), 377–383.

    Article  MATH  MathSciNet  Google Scholar 

  6. M. Morley,The number of countable models, J. Symb. Logic35 (1970), 14–18.

    Article  MATH  MathSciNet  Google Scholar 

  7. J. Saffe,On Vaught’s conjecture for superstable theories, to appear.

  8. J. Saffe,Einige Ergebnisse uber die Auzahl abrahlbarer Modelle superstabiler Theorien, Dissertation, Universitat Hannover, 1981.

Download references

Author information

Author notes

  1. S. Shelah

    Present address: Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel

  2. L. Harrington

    Present address: Department of Mathematics, University of California, 94720, Berkeley, CA, USA

  3. M. Makkai

    Present address: Department of Mathematics, McGill University, H3C 3G1, Montreal, PQ, Canada

Authors and Affiliations

  1. Institute for Advanced Studies, The Hebrew University of Jerusalem, Jerusalem, Israel

    S. Shelah, L. Harrington & M. Makkai

Authors
  1. S. Shelah
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. Harrington
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Makkai
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Dedicated to the memory of Abraham Robinson on the tenth anniversary of his death

The author thanks the United States-Israel Binational Science Foundation for supporting his research.

Supported by the Natural Sciences and Engineering Research Council of Canada, and FCAC Quebec.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shelah, S., Harrington, L. & Makkai, M. A proof of vaught’s conjecture forω-stable theories. Israel J. Math. 49, 259–280 (1984). https://doi.org/10.1007/BF02760651

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02760651

Keywords

Search

Navigation