All you need is A_κ

2025/06/17 by Nathaniel Bannister, Bannister, Nathaniel
Mathematics · #Advanced Operator Algebra Research #Advanced Topology and Set Theory #FOS: Mathematics #Geometry and complex manifolds #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.2506.14185

openalex publication_date 2025/06/17 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/28

Abstract

We show that the vanishing of higher derived limits of the system A_κ implies the additivity of strong homology on the class of locally compact metric spaces of weight at most κ, thereby establishing a converse to a theorem of Mardešić and Prasolov.

Citations

• Simultaneously nonvanishing higher derived limits
• Additivity of derived limits in the Cohen model
• A descriptive approach to higher derived limits
• Non-vanishing higher derived limits
• Simutaneously vanishing higher derived limits without large cardinals
• On the additivity of strong homology for locally compact separable metric spaces
• Strong Homology, Derived Limits, and Set Theory

Related

• Non-vanishing higher derived limits
• On the additivity of strong homology for locally compact separable metric spaces
• Strong Homology, Derived Limits, and Set Theory
• Simutaneously vanishing higher derived limits without large cardinals
• Additivity of derived limits in the Cohen model