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Splitting \({\mathcal P}_\kappa \lambda\) into maximally many stationary sets. (English) Zbl 0955.03047

Let \(\kappa\) be a regular uncountable cardinal and let \(\lambda\) be a cardinal, \(\lambda > \kappa\). In this paper the author shows that \({\mathcal P}_{\kappa}\lambda = \{x\subseteq\lambda : |x|<\kappa\}\) can be decomposed into \(\lambda^{\omega}\) pairwise disjoint stationary sets, and when \(\text{ cf} \lambda < \kappa\) then \({\mathcal P}_{\kappa}\lambda\) can be decomposed into \(\lambda^+\) pairwise disjoint stationary sets.

MSC:

03E05 Other combinatorial set theory
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