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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2312.02623 |
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| _version_ | 1866909329784832000 |
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| author | Šaroch, Jan Trlifaj, Jan |
| author_facet | Šaroch, Jan Trlifaj, Jan |
| contents | We prove a version of Shelah's Categoricity Conjecture for arbitrary deconstructible classes of modules. Moreover, we show that if $\mathcal{A}$ is a deconstructible class of modules that fits in an abstract elementary class $(\mathcal{A},\preceq)$ such that (1) $\mathcal{A}$ is closed under direct summands and (2) $\preceq$ refines direct summands, then $\mathcal{A}$ is closed under arbitrary direct limits. In an Appendix, we prove that the assumption (2) is not needed in some models of ZFC. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_02623 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Deconstructible abstract elementary classes of modules and categoricity Šaroch, Jan Trlifaj, Jan Representation Theory Logic 03C95, 16E30 (primary), 03C35, 16D10 (secondary) We prove a version of Shelah's Categoricity Conjecture for arbitrary deconstructible classes of modules. Moreover, we show that if $\mathcal{A}$ is a deconstructible class of modules that fits in an abstract elementary class $(\mathcal{A},\preceq)$ such that (1) $\mathcal{A}$ is closed under direct summands and (2) $\preceq$ refines direct summands, then $\mathcal{A}$ is closed under arbitrary direct limits. In an Appendix, we prove that the assumption (2) is not needed in some models of ZFC. |
| title | Deconstructible abstract elementary classes of modules and categoricity |
| topic | Representation Theory Logic 03C95, 16E30 (primary), 03C35, 16D10 (secondary) |
| url | https://arxiv.org/abs/2312.02623 |