Splitting ρκλ into maximally many stationary sets

Letκ >ω be a regular cardinal and λ >κ a cardinal. Solovay’s classical result for κSo] led Menas Me] to conjecture that a stationary subset ofP _κλ would split into λ^<κ stationary set of size κ⁺ (seeBT]), the conjecture implies that the size is (κ⁺)^<κ as well. Part of this work was done during the author’s stay at Boston University as one of the Japanese Overseas Research Fellows. He gratefully acknowledge Professor Akihiro Kanamori’s hospitality. He also wishes to thank members of the set theory seminar at Waseda University for their interest at the early stage.