Ineffability of Pκλ for λ with small cofinality

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Abstract

We study ineffability, the Shelah property, and indescribability of P κλ when cf(λ) < κ. We prove that if λ is a strong limit cardinal with cf(λ) < κ then the ineffable ideal, the Shelah ideal, and the completely ineffable ideal over Pκλare the same, and that it can be precipitous. Furthermore we show that Π1/1-indescribability of Pκλ is much stronger than ineffability if 2λ = λ.

Original languageEnglish
Pages (from-to)935-954
Number of pages20
JournalJournal of the Mathematical Society of Japan
Volume60
Issue number3
DOIs
Publication statusPublished - 2008 Jul 1
Externally publishedYes

Keywords

  • Almost ineffable
  • Indescribable
  • Ineffable
  • P λ
  • The Shelah property

ASJC Scopus subject areas

  • Mathematics(all)

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