Distinguishing Internally Club and Approachable on an Infinite Interval
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916219752284160 |
|---|---|
| author | Jakob, Hannes Levine, Maxwell |
| author_facet | Jakob, Hannes Levine, Maxwell |
| contents | Krueger showed that PFA implies that for all regular $Θ\ge \aleph_2$, there are stationarily many $[H(Θ)]^{\aleph_1}$ that are internally club but not internally approachable. From countably many Mahlo cardinals, we force a model in which, for all positive $n<ω$ and $Θ\ge \aleph_{n+1}$, there is a stationary subset of $[H(Θ)]^{\aleph_n}$ consisting of sets that are internally club but not internally approachable. The theorem is obtained using a new variant of Mitchell forcing. This answers questions of Krueger. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_15230 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Distinguishing Internally Club and Approachable on an Infinite Interval Jakob, Hannes Levine, Maxwell Logic 03E35, 03E55 Krueger showed that PFA implies that for all regular $Θ\ge \aleph_2$, there are stationarily many $[H(Θ)]^{\aleph_1}$ that are internally club but not internally approachable. From countably many Mahlo cardinals, we force a model in which, for all positive $n<ω$ and $Θ\ge \aleph_{n+1}$, there is a stationary subset of $[H(Θ)]^{\aleph_n}$ consisting of sets that are internally club but not internally approachable. The theorem is obtained using a new variant of Mitchell forcing. This answers questions of Krueger. |
| title | Distinguishing Internally Club and Approachable on an Infinite Interval |
| topic | Logic 03E35, 03E55 |
| url | https://arxiv.org/abs/2404.15230 |