Splitting stationary sets in $𝓟_{κ}λ$ for λ with small cofinality

• Autorzy: Toshimichi Usuba
• Języki publikacji: EN

Abstrakty

EN

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 $𝓟_{κ}λ$ 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 $𝓟_{κ}λ$ such that every stationary subset of S can be split into λ⁺ many pairwise disjoint stationary subsets.

Kategorie tematyczne

• 03E55: Large cardinals
• 03E05: Other combinatorial set theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2009
• Tom: 205
• Numer: 3
• Strony: 265-287

Daty

wydano

2009

Twórcy

autor

Toshimichi Usuba

• Hausdorff Center for Mathematics, University of Bonn, 53115 Bonn, Germany

Identyfikatory

DOI

10.4064/fm205-3-4