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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Less saturated ideals


Authors: Moti Gitik and Saharon Shelah
Journal: Proc. Amer. Math. Soc. 125 (1997), 1523-1530
MSC (1991): Primary 03E35, 03E40, 04A20
DOI: https://doi.org/10.1090/S0002-9939-97-03702-7
MathSciNet review: 1363421
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Abstract:

We prove the following:

  • [(1)] If $\kappa$ is weakly inaccessible then $NS_{\kappa }$ is not $\kappa ^{+}$-saturated.

  • [(2)] If $\kappa$ is weakly inaccessible and $\theta < \kappa$ is regular then $NS^{\theta }_{\kappa }$ is not $\kappa ^{+}$-saturated.

  • [(3)] If $\kappa$ is singular then $NS^{cf \kappa }_{ \kappa ^{+}}$ is not $\kappa ^{++}$-saturated.

  • Combining this with previous results of Shelah, one obtains the following:

  • [(A)] If $\kappa >\aleph _{1}$ then $NS_{\kappa }$ is not $\kappa ^{+}$-saturated.

  • [(B)] If $\theta ^{+}< \kappa$ then $NS^{\theta }_{\kappa }$ is not $\kappa ^{+}$-saturated.


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    Additional Information

    Moti Gitik
    Affiliation: School of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv 69978, Israel
    MR Author ID: 74045
    Email: gitik@math.tau.ac.il

    Saharon Shelah
    Affiliation: Hebrew University of Jerusalem, Department of Mathematics, Givat Ram, Jerusalem, Israel
    MR Author ID: 160185
    ORCID: 0000-0003-0462-3152
    Email: shelah@math.huji.ac.il

    Received by editor(s): March 1, 1995
    Received by editor(s) in revised form: November 20, 1995
    Additional Notes: The second author was partially supported by the Basic Research Fund, Israel Academy of Sciences.
    This is number 577 in the cumulative list of the second author’s publications.
    Communicated by: Andreas R. Blass
    Article copyright: © Copyright 1997 American Mathematical Society