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Proceedings of the American Mathematical Society
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
MathSciNet review: 1363421
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Abstract | References | Similar Articles | Additional Information

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
Email: gitik@math.tau.ac.il

Saharon Shelah
Affiliation: Hebrew University of Jerusalem, Department of Mathematics, Givat Ram, Jerusalem, Israel
Email: shelah@math.huji.ac.il

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03702-7
PII: S 0002-9939(97)03702-7
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