Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.18603 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916337253613568 |
|---|---|
| author | Feldman, Ido |
| author_facet | Feldman, Ido |
| contents | Justin Moore's weak club-guessing principle $\mho$ admits various possible generalizations to the second uncountable cardinal. One of them was shown to hold in ZFC by Shelah. A stronger one was shown to follow from several consequences of the continuum hypothesis by Inamdar and Rinot. Here we prove that the stronger one may consistently fail. Specifically, starting with a supercompact cardinal and an inaccessible cardinal above it, we devise a notion of forcing consisting of finite working parts and finitely many two types of models as side conditions, to violate this analog of $\mho$ at the second uncountable cardinal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_18603 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Failure of an higher analogue of Mho Feldman, Ido Logic Justin Moore's weak club-guessing principle $\mho$ admits various possible generalizations to the second uncountable cardinal. One of them was shown to hold in ZFC by Shelah. A stronger one was shown to follow from several consequences of the continuum hypothesis by Inamdar and Rinot. Here we prove that the stronger one may consistently fail. Specifically, starting with a supercompact cardinal and an inaccessible cardinal above it, we devise a notion of forcing consisting of finite working parts and finitely many two types of models as side conditions, to violate this analog of $\mho$ at the second uncountable cardinal. |
| title | Failure of an higher analogue of Mho |
| topic | Logic |
| url | https://arxiv.org/abs/2407.18603 |