On the non-existence of κ-mad families

2019/06/23 by Haim Horowitz, Saharon Shelah, Horowitz, Haim +1
Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1906.09538

openalex publication_date 2019/06/23 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

Starting from a model with a Laver-indestructible supercompact cardinal κ, we construct a model of ZF+DC_κ where there are no κ-mad families.

Related

• κ-Madness and Definability.
• Madness and regularity properties
• All uncountable regular cardinals can be inaccessible in HOD
• Strong Tree Properties for Small Cardinals
• Mad families and non-meager filters