### 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
^{, 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 |
---|---|

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 |

Externally published | Yes |

### Fingerprint

### Keywords

- Ineffability
- Pκλ
- Partition property

### ASJC Scopus subject areas

- Logic
- Philosophy

### Cite this

*Archive for Mathematical Logic*,

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

**Notes on the partition property of Pκλ.** / Abe, Yoshihiro; Usuba, Toshimichi.

Research output: Contribution to journal › Article

*Archive for Mathematical Logic*, vol. 51, no. 5-6, pp. 575-589. https://doi.org/10.1007/s00153-012-0283-x

}

TY - JOUR

T1 - Notes on the partition property of Pκλ

AU - Abe, Yoshihiro

AU - Usuba, Toshimichi

PY - 2012/8

Y1 - 2012/8

N2 - 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 , 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.

AB - 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 , 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.

KW - Ineffability

KW - Pκλ

KW - Partition property

UR - http://www.scopus.com/inward/record.url?scp=84864375707&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84864375707&partnerID=8YFLogxK

U2 - 10.1007/s00153-012-0283-x

DO - 10.1007/s00153-012-0283-x

M3 - Article

AN - SCOPUS:84864375707

VL - 51

SP - 575

EP - 589

JO - Archive for Mathematical Logic

JF - Archive for Mathematical Logic

SN - 0933-5846

IS - 5-6

ER -