Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.00310 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912378407354368 |
|---|---|
| author | Kowalczyk, Jacob |
| author_facet | Kowalczyk, Jacob |
| contents | It is consistent with ZF + DC that there exists an ultrafilter $U$ on $ω$ such that two infinite ultraproducts of finite sets, $\prod A_n / U$ and $\prod B_n / U$, have the same cardinality if and only if $0 < \lim_U |A_n|/|B_n| < \infty$. In particular, this holds in $W[U]$, where $W$ is the Solovay Model and $U$ is $[ω]^ω$-generic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_00310 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cardinalities of Ultraproducts of Finite Sets in ZF + DC Kowalczyk, Jacob Logic It is consistent with ZF + DC that there exists an ultrafilter $U$ on $ω$ such that two infinite ultraproducts of finite sets, $\prod A_n / U$ and $\prod B_n / U$, have the same cardinality if and only if $0 < \lim_U |A_n|/|B_n| < \infty$. In particular, this holds in $W[U]$, where $W$ is the Solovay Model and $U$ is $[ω]^ω$-generic. |
| title | Cardinalities of Ultraproducts of Finite Sets in ZF + DC |
| topic | Logic |
| url | https://arxiv.org/abs/2503.00310 |