SPLITTING STATIONARY SETS IN Ρ(λ).

Let A be a non-empty set. A set S ⊆ 풫(A) is said to be stationary in 풫(A) if for every ƒ: [A]^<ω → A there exists x ∈ S such that x ≠ A and ƒ"[x]^<ω ⊆ x. In this paper we prove the following: For an uncountable cardinal λ and a stationary set S in 풫(λ), if there is a regular uncountable cardinal κ ≤ λ such that {x ∈ S : x ∩ κ ∈ κ} is stationary, then S can be split into κ disjoint stationary subsets. [ABSTRACT FROM AUTHOR]