Israel Journal of Mathematics

, Volume 29, Issue 4, pp 385–388 | Cite as

Making the supercompactness of κ indestructible under κ-directed closed forcing

  • Richard Laver


A model is found in which there is a supercompact cardinal κ which remains supercompact in any κ-directed closed forcing extension.


Partial Order Choice Function Inverse Limit Force Extension Regular Cardinal 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    W. B. Easton,Powers of regular cardinals, Ann. Math. Logic1 (1970), 139–178.zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    A. Kanamori, W. Reinhardt and R. Solovay,Strong axioms of infinity and elementary embeddings, to appear in Ann. Math. Logic.Google Scholar
  3. 3.
    K. Kunen and J. Paris,Boolean extensions and measurable cardinals, Ann. Math. Logic2 (1971), 359–377.zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    T. Menas,Consistency results concerning supercompactness, Trans. Amer. Math. Soc.223 (1976), 61–91.zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    T. Menas,A combinatorial property of P κ λ, J. Symbolic Logic41 (1976), 225–234.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Hebrew University 1978

Authors and Affiliations

  • Richard Laver
    • 1
  1. 1.Department of MathematicsUniversity of ColoradoBoulderUSA

Personalised recommendations