Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Less Saturated Ideals

Author(s): Moti Gitik; Saharon Shelah
Journal: Proc. Amer. Math. Soc. 125 (1997), 1523-1530.
MSC (1991): Primary 03E35, 03E40, 04A20
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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