## Journal of Symbolic Logic

### Splitting stationary sets in $\mathscr{P}(\lambda)$

Toshimichi Usuba

#### Abstract

Let $A$ be a non-empty set. $A$ set $S \subseteq \mathscr{P}(A)$ is said to be stationary in $\mathscr{P}(A)$ if for every $f: [A]^{< \omega} \to A$ there exists $x \in S$ such that $x \neq A$ and $f"[x]^{<\omega}$. In this paper we prove the following: For an uncountable cardinal ? and a stationary set S in $\mathscr{P}(\lambda)$, if there is a regular uncountable cardinal $k \leq \lambda$ such that $\{x \in S: x \cap k \in k\}$ is stationary, then S can be split into $k$ disjoint stationary subsets.

#### Article information

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

Dates
First available in Project Euclid: 20 January 2012

https://projecteuclid.org/euclid.jsl/1327068691

Digital Object Identifier
doi:10.2178/jsl/1327068691

Mathematical Reviews number (MathSciNet)
MR2951629

Zentralblatt MATH identifier
1250.03077

Subjects
Primary: Primary 03E05; Secondary 03E55

#### Citation

Usuba, Toshimichi. Splitting stationary sets in $\mathscr{P}(\lambda)$. J. Symbolic Logic 77 (2012), no. 1, 49--62. doi:10.2178/jsl/1327068691. https://projecteuclid.org/euclid.jsl/1327068691

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