Consistency of "the ideal of null restricted to some A is kappa-complete not kappa⁺-complete, kappa weakly inaccessible and cov(meagre)=aleph₁"

2005/04/10 by Saharon Shelah, Shelah, Saharon
Mathematics · #Advanced Topology and Set Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Logic (math.LO) #Rings, Modules, and Algebras #math.LO

paper · pdf · doi:10.48550/arxiv.math/0504201

arxiv created 2005/04/10 · openalex publication_date 2005/04/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we answer the following question of Grinblat: Is it consistent that for some set X, cov(NULL restriction X)=lambda is a weakly inaccessible cardinal (so X not null of course) while cov(meagre) is small, say it is aleph₁.

Related

• Cardinal preserving ideals
• A parallel to the null ideal for inaccessible lambda. Part I
• On CON(\mathfrak d_λ> cov_λ(meagre))
• On CON(Dominating_lambda > cov_λ(meagre))
• The null ideal restricted to some non-null set may be ℵ₁-saturated