Expressive power of infinitary logic and absolute co-Hopfianity

Mohsen Asgharzadeh, Mohammad Golshani, Saharon Shelah

Research output: Contribution to journalArticlepeer-review

Abstract

Recently, Paolini and Shelah 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.

Original languageEnglish
Pages (from-to)269-302
Number of pages34
JournalIllinois Journal of Mathematics
Volume69
Issue number2
DOIs
StatePublished - 1 Jun 2025

Bibliographical note

Publisher Copyright:
© 2025 by the University of Illinois Urbana-Champaign.

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