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<κ.
ASJC Scopus subject areas
- 数学 (全般)