Nowhere precipitousness of the non-stationary ideal over ${\mathcal P}_{\kappa}\lambda$

by Matsubara and Shelah. [MsSh:758]
J Math Logic, 2002
We prove that if lambda is a strong limit singular cardinal and kappa a regular uncountable cardinal < lambda, then NS_{kappa lambda}, the non-stationary ideal over P_{kappa} lambda, is nowhere precipitous. We also show that under the same hypothesis every stationary subset of P_{kappa} lambda can be partitioned into lambda^{< kappa} disjoint stationary sets.


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