The higher Cichon diagram in the degenerate case

2019/07/06 by Joerg Brendle, Brendle, Joerg
Mathematics · #03E17 (Primary) 03E05 #03E35 (Secondary) #Advanced Topology and Set Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Logic (math.LO) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1907.03111

openalex publication_date 2019/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a regular uncountable cardinal kappa, we discuss the order relationship between the unbounding and dominating numbers on kappa and cardinal invariants of the higher meager ideal M_kappa. In particular, we obtain a complete characterization of add(M_kappa) and cof(M_kappa) in terms of cov(M_kappa) and non(M_kappa) and unbounding and dominating numbers, and we provide models showing that there are no restrictions on the value of non(M_kappa) in the degenerate case 2^ kappa except 2^

Related

• Cichoń's maximum without large cardinals
• Cichon's Diagram for uncountable cardinals
• Higher Dimensional Cardinal Characteristics for Sets of Functions II
• Cardinal invariants associated with the combinatorics of the uniformity number of the ideal of meager-additive sets
• The Horizontal Direction