Sh:1246
- Asgharzadeh, M., Golshani, M., & Shelah, S. (2025). Expressive power of infinitary logic and absolute co-Hopfianity. Illinois J. Math, 69(2), 269–302. arXiv: 2309.16997 MR: 4919937
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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 (41p)
Bib entry
@article{Sh:1246, author = {Asgharzadeh, Mohsen and Golshani, Mohammad and Shelah, Saharon}, title = {{Expressive power of infinitary logic and absolute co-Hopfianity}}, journal = {Illinois J. Math}, volume = {69}, number = {2}, year = {2025}, pages = {269--302}, mrnumber = {4919937}, note = {\href{https://arxiv.org/abs/2309.16997}{arXiv: 2309.16997}}, arxiv_number = {2309.16997} }