Lietz, A. T. (2024, October 8). Forcing “NS_{ω_1} is ω_1-dense” from large cardinals - a journey guided by the stars [Conference Presentation]. Colloquium Logicum 2024, Wien, Austria.
The nonstationary ideal on ω_1 is ω_1-dense if there is a set B of ω_1-many stationary subsets of ω_1 that every stationary subset of ω_1 contains an element of S on a club. We show that this principle holds true in a stationary set preserving forcing extension, assuming a supercompact limit of supercompact cardinals exists. This answers a question of Woodin positively.
