Notes on the partition property of Pκλ

Yoshihiro Abe, Toshimichi Usuba

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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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Keywords

  • Ineffability
  • Pκλ
  • Partition property

ASJC Scopus subject areas

  • Logic
  • Philosophy

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