Less saturated ideals

by Gitik and Shelah. [GiSh:577]
Proc American Math Soc, 1997
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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