Sh:1246

• Asgharzadeh, M., Golshani, M., & Shelah, S. Expressive power of infinitary logic and absolute co-Hopfianity. Preprint. arXiv: 2309.16997
• 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 apply the infinitary logic to show a dichotomy behavior of co-Hopfian groups, by showing that the first beautiful cardinal is the turning point for this property. Namely, we prove 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.
• Version 2023-11-28 (45p)

@article{Sh:1246,
 author = {Asgharzadeh, Mohsen and Golshani, Mohammad and Shelah, Saharon},
 title = {{Expressive power of infinitary logic and absolute co-Hopfianity}},
 note = {\href{https://arxiv.org/abs/2309.16997}{arXiv: 2309.16997}},
 arxiv_number = {2309.16997}
}