For a regular uncountable cardinal κ and a cardinal λ with cf(λ) < κ < λ, we investigate the consistency strength of the existence of a stationary set in which cannot be split into λ⁺ 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 such that every stationary subset of S can be split into λ⁺ many pairwise disjoint stationary subsets.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm205-3-4,
author = {Toshimichi Usuba},
title = {Splitting stationary sets in $\_{$\kappa$}$\lambda$$ for $\lambda$ with small cofinality},
journal = {Fundamenta Mathematicae},
volume = {205},
year = {2009},
pages = {265-287},
zbl = {1280.03049},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm205-3-4}
}
Toshimichi Usuba. Splitting stationary sets in $_{κ}λ$ for λ with small cofinality. Fundamenta Mathematicae, Tome 205 (2009) pp. 265-287. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm205-3-4/