Almost refinement, reaping, and ultrafilter numbers
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915756694831104 |
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| author | Brendle, Jörg Hrušák, Michael Parente, Francesco |
| author_facet | Brendle, Jörg Hrušák, Michael Parente, Francesco |
| contents | We investigate the combinatorial structure of the set of maximal antichains in a Boolean algebra ordered by almost refinement. We also consider the reaping relation and its associated cardinal invariants, focusing in particular on reduced powers of Boolean algebras. As an application, we obtain that, on the one hand, the ultrafilter number of the Cohen algebra is greater than or equal to the cofinality of the meagre ideal and, on the other hand, a suitable parametrized diamond principle implies that the ultrafilter number of the Cohen algebra is equal to $\aleph_1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_18595 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Almost refinement, reaping, and ultrafilter numbers Brendle, Jörg Hrušák, Michael Parente, Francesco Logic 03E05 (Primary) 03E17, 06E99 (Secondary) We investigate the combinatorial structure of the set of maximal antichains in a Boolean algebra ordered by almost refinement. We also consider the reaping relation and its associated cardinal invariants, focusing in particular on reduced powers of Boolean algebras. As an application, we obtain that, on the one hand, the ultrafilter number of the Cohen algebra is greater than or equal to the cofinality of the meagre ideal and, on the other hand, a suitable parametrized diamond principle implies that the ultrafilter number of the Cohen algebra is equal to $\aleph_1$. |
| title | Almost refinement, reaping, and ultrafilter numbers |
| topic | Logic 03E05 (Primary) 03E17, 06E99 (Secondary) |
| url | https://arxiv.org/abs/2410.18595 |