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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.
Toshimichi Usuba. "Splitting stationary sets in $_{κ}λ$ for λ with small cofinality." Fundamenta Mathematicae 205.3 (2009): 265-287. <http://eudml.org/doc/282643>.
@article{ToshimichiUsuba2009, abstract = {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 $_\{κ\}λ$ 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 $_\{κ\}λ$ such that every stationary subset of S can be split into λ⁺ many pairwise disjoint stationary subsets.}, author = {Toshimichi Usuba}, journal = {Fundamenta Mathematicae}, language = {eng}, number = {3}, pages = {265-287}, title = {Splitting stationary sets in $_\{κ\}λ$ for λ with small cofinality}, url = {http://eudml.org/doc/282643}, volume = {205}, year = {2009}, }
TY - JOUR AU - Toshimichi Usuba TI - Splitting stationary sets in $_{κ}λ$ for λ with small cofinality JO - Fundamenta Mathematicae PY - 2009 VL - 205 IS - 3 SP - 265 EP - 287 AB - 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 $_{κ}λ$ 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 $_{κ}λ$ such that every stationary subset of S can be split into λ⁺ many pairwise disjoint stationary subsets. LA - eng UR - http://eudml.org/doc/282643 ER -