Splitting stationary sets in ${\cal P}_{\kappa} \lambda$ for $\lambda$ with small cofinality
Tom 205 / 2009
Fundamenta Mathematicae 205 (2009), 265-287
MSC: Primary 03E05; Secondary 03E55
DOI: 10.4064/fm205-3-4
Streszczenie
For a regular uncountable cardinal $\kappa$ and a cardinal $\lambda$ with ${\rm cf}(\lambda)<\kappa <\lambda$, we investigate the consistency strength of the existence of a stationary set in ${\cal P}_\kappa \lambda$ which cannot be split into $\lambda^+$ many pairwise disjoint stationary subsets. To do this, we introduce a new notion for ideals, which is a variation of normality of ideals. We also prove that there is a stationary set $S$ in ${\cal P}_\kappa \lambda$ such that every stationary subset of $S$ can be split into $\lambda^+$ many pairwise disjoint stationary subsets.
