Expressive Power of Infinitary Logic and Absolute co-Hopfianity
Logic
2024-11-28 v2 Commutative Algebra
Group Theory
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.
Cite
@article{arxiv.2309.16997,
title = {Expressive Power of Infinitary Logic and Absolute co-Hopfianity},
author = {Mohsen Asgharzadeh and Mohammad Golshani and Saharon Shelah},
journal= {arXiv preprint arXiv:2309.16997},
year = {2024}
}