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arXiv · 2309.16997

Expressive Power of Infinitary Logic and Absolute co-Hopfianity

Mohsen Asgharzadeh·Mohammad Golshani·Saharon Shelah
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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 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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Mohsen Asgharzadeh, Mohammad Golshani, Saharon Shelah. 2023-09-29. Expressive Power of Infinitary Logic and Absolute co-Hopfianity. https://arxiv.org/abs/2309.16997

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