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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2302.07222 |
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| _version_ | 1866909463401725952 |
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| author | Bannister, Nathaniel |
| author_facet | Bannister, Nathaniel |
| contents | We show that, in the model constructed by adding sufficiently many Cohen reals, derived limits are additive on a large class of systems. This generalizes the work of Jeffrey Bergfalk, Michael Hru\v sák, and Chris Lambie-Hanson which focuses on the system $\mathbf{A}$. In the process, we isolate a partition principle responsible for the vanishing of derived limits on collections of Cohen reals and reframe the propagating trivializations results of Bergfalk, Hru\v sák and Lambie-Hanson as a theorem of ZFC. In light of results of the author, Jeffrey Bergfalk, and Justin Moore, the additivity of derived limits also implies additivity results for strong homology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_07222 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Additivity of derived limits in the Cohen model Bannister, Nathaniel Logic We show that, in the model constructed by adding sufficiently many Cohen reals, derived limits are additive on a large class of systems. This generalizes the work of Jeffrey Bergfalk, Michael Hru\v sák, and Chris Lambie-Hanson which focuses on the system $\mathbf{A}$. In the process, we isolate a partition principle responsible for the vanishing of derived limits on collections of Cohen reals and reframe the propagating trivializations results of Bergfalk, Hru\v sák and Lambie-Hanson as a theorem of ZFC. In light of results of the author, Jeffrey Bergfalk, and Justin Moore, the additivity of derived limits also implies additivity results for strong homology. |
| title | Additivity of derived limits in the Cohen model |
| topic | Logic |
| url | https://arxiv.org/abs/2302.07222 |