Forcing Diamond and Applications to Iterability
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908313844711424 |
|---|---|
| author | Mildenberger, Heike Shelah, Saharon |
| author_facet | Mildenberger, Heike Shelah, Saharon |
| contents | We show that higher Sacks forcing at a regular limit cardinal and club Miller forcing at an uncountable regular cardinal both add a diamond sequence.
We answer the longstanding question, whether $κ= κ^{<κ} \geq\aleph_1$ implies that $κ$-supported iterations of $κ$-Sacks forcing do not collapse $κ^+$ and are $κ$-proper in the affirmative. The results pertain to other higher tree forcings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_08390 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Forcing Diamond and Applications to Iterability Mildenberger, Heike Shelah, Saharon Logic 03E35, 03E05 We show that higher Sacks forcing at a regular limit cardinal and club Miller forcing at an uncountable regular cardinal both add a diamond sequence. We answer the longstanding question, whether $κ= κ^{<κ} \geq\aleph_1$ implies that $κ$-supported iterations of $κ$-Sacks forcing do not collapse $κ^+$ and are $κ$-proper in the affirmative. The results pertain to other higher tree forcings. |
| title | Forcing Diamond and Applications to Iterability |
| topic | Logic 03E35, 03E05 |
| url | https://arxiv.org/abs/2504.08390 |