### Abstract

We investigate the partition property of Pκλ. Main results of this paper are as follows: (1) If λ is the least cardinal greater than κ such that Pκλ carries a (λ ^{<κ}, 2)-distributive normal ideal without the partition property, then λ is Π _{n} ^{1}-indescribable for all n < ω but not Π _{1} ^{2} -indescribable. (2) If cf(λ) ≥ κ, then every ineffable subset of Pκλ has the partition property. (3) If cf(λ) ≥ κ, then the completely ineffable ideal over Pκλ has the partition property.

Original language | English |
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Pages (from-to) | 575-589 |

Number of pages | 15 |

Journal | Archive for Mathematical Logic |

Volume | 51 |

Issue number | 5-6 |

DOIs | |

Publication status | Published - 2012 Aug 1 |

Externally published | Yes |

### Keywords

- Ineffability
- Partition property
- Pκλ

### ASJC Scopus subject areas

- Philosophy
- Logic

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## Cite this

Abe, Y., & Usuba, T. (2012). Notes on the partition property of Pκλ.

*Archive for Mathematical Logic*,*51*(5-6), 575-589. https://doi.org/10.1007/s00153-012-0283-x