Israel Journal of Mathematics

, Volume 7, Issue 3, pp 187–202 | Cite as

Stable theories

  • S. Shelah


We studyK T(λ)=sup {|S(A)| : |A|≦λ} and extend some results for totally transcendental theroies to the case of stable theories. We then investigate categoricity of elementary and pseudo-elementary classes.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    H. J. Keisler,Some model theoretic results for w-logic, Israel J. of Math.4(1966), 249–261.MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    M. Morley,Categoricity in power, Trans. Amer. Math. Soc.114 (1965), 514–538.MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    M. Morley,Omitting classes of elements, The theory of models, Proceedings of the 1964 International Symp., North-Holland Publishing Company (1965), 265–274.Google Scholar
  4. 4.
    M. Morley and R. L. Vaught,Homogeneous universal models, Mathematica Scandinavia11 (1962), 37–57.MATHMathSciNetGoogle Scholar
  5. 5.
    J. P. Ressayre,Sur les théories du premier ordre catégorique en un cardinal, mimeograph, Paris.Google Scholar
  6. 6.
    F. Rowbottom,The Lo’s conjecture for uncountable theories, Notices of the Amer. Math. Soc.11 (1964), 248.Google Scholar
  7. 7.
    S. Shelah,Classes with homogeneous models only, Notices of the Amer. Math. Soc.15 (1968), 803.Google Scholar
  8. 8.
    S. Shelah,Categoricity in power, Notices of the Amer. Math. Soc.15 (1968), 903.Google Scholar
  9. 9.
    R. L. Vaught,The Löwenheim-Skolem theorem, Logic Methodology and Philosophy of Science, Proceedings of the 1964 International Congress, North-Holland Publishing Company, Amsterdam (1965), 81–89.Google Scholar

Copyright information

© The Weizmann Science Press of Israel 1969

Authors and Affiliations

  • S. Shelah
    • 1
  1. 1.The Hebrew University of JerusalemIsrael

Personalised recommendations