Splitting stationary sets in ${}_{\kappa }\lambda$ for λ with small cofinality

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 -