Geodesic
Splitting stationary sets in ${\cal P}_{\kappa} \lambda$ for $\lambda$ with small cofinality
Toshimichi Usuba1
1 Hausdorff Center for Mathematics University of Bonn 53115 Bonn, Germany
Fundamenta Mathematicae, Tome 205 (2009) no. 3, pp. 265-287.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/fm205-3-4
Keywords: regular uncountable cardinal kappa cardinal lambda lambda kappa lambda investigate consistency strength existence stationary set cal kappa lambda which cannot split lambda many pairwise disjoint stationary subsets introduce notion ideals which variation normality ideals prove there stationary set cal kappa lambda every stationary subset split lambda many pairwise disjoint stationary subsets

Toshimichi Usuba 1

1 Hausdorff Center for Mathematics University of Bonn 53115 Bonn, Germany 
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Toshimichi Usuba. Splitting stationary sets in ${\cal P}_{\kappa} \lambda$
for $\lambda$ with small cofinality. Fundamenta Mathematicae, Tome 205 (2009) no. 3, pp. 265-287. doi : 10.4064/fm205-3-4. http://geodesic.mathdoc.fr/articles/10.4064/fm205-3-4/

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