Notes on the partition property of Pκλ

Yoshihiro Abe, Toshimichi Usuba

Research output: Contribution to journalArticle

2 Citations (Scopus)

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 languageEnglish
Pages (from-to)575-589
Number of pages15
JournalArchive for Mathematical Logic
Volume51
Issue number5-6
DOIs
Publication statusPublished - 2012 Aug
Externally publishedYes

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Partition
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Ideal

Keywords

  • Ineffability
  • Pκλ
  • Partition property

ASJC Scopus subject areas

  • Logic
  • Philosophy

Cite this

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

In: Archive for Mathematical Logic, Vol. 51, No. 5-6, 08.2012, p. 575-589.

Research output: Contribution to journalArticle

Abe, Yoshihiro ; Usuba, Toshimichi. / Notes on the partition property of Pκλ. In: Archive for Mathematical Logic. 2012 ; Vol. 51, No. 5-6. pp. 575-589.
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