Israel Journal of Mathematics

, Volume 48, Issue 4, pp 257–288 | Cite as

The nonstationary ideal on ℵ2

  • Moti Gitik


We construct a model in which the filter of ω-closed unbounded subsets of ℵ2 is precipitous and a model in which the filter of closed unbounded subsets of ℵ2 is precipitous. For the first model we need a measurable cardinal, and for the second a measurable cardinal of order 2. Both results are equiconsistent.


Dense Subset Generic Subset Measurable Cardinal Force Notion Elementary Chain 
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.
    U. Avraham and S. Shelah,Forcing closed unbounded sets, J. Sym. Log.48 (1983), 643–648.CrossRefGoogle Scholar
  2. 2.
    J. Baumgartner,A new kind of order types, Ann. Math. Log.9 (1976), 187–222.MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    J. Baumgartner, L. Harrington and E. M. Kleinberg,Adding a closed unbounded set, J. Sym. Log.41 (1976), 481–482.MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    K. J. Devlin,Indescribability properties and small large cardinals, inLogic Conference, Kiel 1974, Lecture Notes in Math.499, Springer, Berlin, 1975, pp. 89–117.Google Scholar
  5. 5.
    M. Gitik and S. Shelah,On the  -condition, Isr. J. Math.48 (1984), 148–158.MATHMathSciNetGoogle Scholar
  6. 6.
    T. Jech,Set Theory, Academic Press, 1978.Google Scholar
  7. 7.
    T. Jech, M. Magidor, W. Mitchell and K. Prikry,Precipitous ideals, J. Symb. Log.45 (1980), 1–8.MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    A. Kanamori and M. Magidor,The evolution of large cardinal axioms in set theory, inHigher Set Theory, Lecture Notes in Math.669, Springer, Berlin, 1978, pp. 99–275.CrossRefGoogle Scholar
  9. 9.
    K. Kunen and J. Paris,Boolean extensions and measurable cardinals Ann. Math. Log.2 (1971), 359–378.MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    A. Lévy,The sizes of the indescribable cardinals, inAxiomatic Set Theory (D. S. Scott, ed.), Proc. Symp. Pure Math.13 (1), Am. Math. Soc., Providence, RI, 1971, pp. 205–218.Google Scholar
  11. 11.
    W. Mitchell,The core model for sequences of measures, to appear.Google Scholar
  12. 12.
    S. Shelah,Iterated forcing and changing cofinalities, Isr. J. Math,40 (1981), 1–32.Google Scholar
  13. 13.
    S. Shelah,Iterated Forcing and Changing Cofinalities II, preprint.Google Scholar
  14. 14.
    S. Shelah,Proper Forcing, Lecture Notes in Math.940, Springer, Berlin, 1982.MATHGoogle Scholar
  15. 15.
    T. Jech,Stationary subsets of inaccessible cardinals, to appear.Google Scholar

Copyright information

© The Weizmann Science Press of Israel 1984

Authors and Affiliations

  • Moti Gitik
    • 1
  1. 1.Department of MathematicsCalifornia Institute of TechnologyPasadenaUSA

Personalised recommendations