Kaethe Minden (Bard College at Simon's Rock) – The Stationary Splitting Number

A splitting family at a regular cardinal kappa is defined so that for any subset X of kappa of size kappa there is a member of the family Y which splits X, namely, both X intersect Y and X - Y have size kappa. The splitting number for kappa is the least size of a splitting family at kappa. Large splitting numbers imply an amount of compactness for kappa (from work of Suzuki). Moreover, forcing can increase the splitting number at supercompact kappa (via Zapletal, credited to Kamo).

I will introduce the stationary splitting number, the least size of a stationary splitting family, which is a family of subsets of kappa splitting stationary subsets into sets that are both stationary. This came up during work with Fuchs on what we call Split Principles, and I will give some background on those, and compare the stationary splitting number to the splitting number and what seems to be known.