### 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]<ω → A there exists x ∈ S such that x ≠ A and f"[x]<ω ⊆ 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 k ≤ λ such that {x ∈ S : x ∩ k ∈ k} is stationary, then S can be split into k disjoint stationary subsets.

Original language | English |
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Pages (from-to) | 49-62 |

Number of pages | 14 |

Journal | Journal of Symbolic Logic |

Volume | 77 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2012 Mar 1 |

Externally published | Yes |

### Keywords

- Pcf-theory
- Saturated ideal
- Stationary set

### ASJC Scopus subject areas

- Philosophy
- Logic

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## Cite this

Usuba, T. (2012). Splitting stationary sets in p(λ).

*Journal of Symbolic Logic*,*77*(1), 49-62. https://doi.org/10.2178/jsl/1327068691