### 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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