### Splitting stationary sets in 𝒫(λ)

Toshimichi Usuba
Source: J. Symbolic Logic Volume 77, Issue 1 (2012), 49-62.

#### Abstract

Let A be a non-empty set. A set S ⊆ 𝒫(A) is said to be stationary in 𝒫(A) if for every f: [A] → A there exists x ∈ S such that x ≠ A and f[x] ⊆ x. In this paper we prove the following: For an uncountable cardinal λ and a stationary set S in 𝒫(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.

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Primary Subjects: Primary 03E05; Secondary 03E55