Less nonstationary ideals

1995/03/01 by Moti Gitik, Saharon Shelah, Gitik, Moti +1
Mathematics · #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Logic (math.LO) #Rings, Modules, and Algebras #math.LO

paper · pdf · doi:10.48550/arxiv.math/9503203

published as Proc. Amer. Math. Soc. 125 No. 5 (1997) 1523--1530

arxiv created 1995/03/01 · openalex publication_date 1995/03/01 · arxiv updated 2016/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We are proving the following: (1) If \kap is a weakly inaccessible then NS_\kap is not \kap⁺-saturated. (2) If \kap is a weakly inaccessible and \tet <\kap is regular then NS^\tet_\kap is not \kap⁺-saturated. (3) If \kap is singular then NS^cf\kap_\kap⁺ is not \kap⁺⁺-saturated. Combining this with previous results of Shelah, one obtains the following: (A) If \kap >ℵ₁ then NS_\kap is not \kap⁺-saturated. (B) If \tet⁺<\kap then NS^\tet_\kap is not \kap⁺-saturated.

Related

• Some results on nonstationry ideal 2
• Consistency of "the ideal of null restricted to some A is kappa-complete not kappa⁺-complete, kappa weakly inaccessible and cov(meagre)=aleph₁"
• On the universality of the nonstationary ideal
• Projective Wellorders and the Nonstationary Ideal
• The extent of saturation of induced ideals