Expressive Power of Infinitary Logic and Absolute co-Hopfianity

2023/09/29 by Mohsen Asgharzadeh, Mohammad Golshani, Asgharzadeh, Mohsen +3
Mathematics · #Advanced Topology and Set Theory #Commutative Algebra (math.AC) #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2309.16997

openalex publication_date 2023/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Recently, Paolini and Shelah have constructed absolutely Hopfian torsion-free abelian groups of any given size. In contrast, we show that this is not necessarily the case for absolutely co-Hopfian groups. We use the infinitary logic to show that there are no absolute co-Hopfian abelian groups above the first beautiful cardinal. An extension of this result to the category of modules over a commutative ring is given.

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