Expressive Power of Infinitary Logic and Absolute co-Hopfianity
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916497207590912 |
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| author | Asgharzadeh, Mohsen Golshani, Mohammad Shelah, Saharon |
| author_facet | Asgharzadeh, Mohsen Golshani, Mohammad Shelah, Saharon |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_16997 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Expressive Power of Infinitary Logic and Absolute co-Hopfianity Asgharzadeh, Mohsen Golshani, Mohammad Shelah, Saharon Logic Commutative Algebra Group Theory 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. |
| title | Expressive Power of Infinitary Logic and Absolute co-Hopfianity |
| topic | Logic Commutative Algebra Group Theory |
| url | https://arxiv.org/abs/2309.16997 |