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| Main Author: | |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2209.12258 |
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| _version_ | 1866917346013085696 |
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| author | Levine, Maxwell |
| author_facet | Levine, Maxwell |
| contents | We introduce a forcing that adds a $\square(\aleph_2,\aleph_0)$-sequence with countable conditions under CH. Assuming the consistency of a weakly compact cardinal, we can find a forcing extension by our new poset in which both $\square(\aleph_2,<\!\aleph_0)$ and $\square_{\aleph_1,\aleph_0}$ fail in the forcing extension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_12258 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Unthreadability with Small Conditions Levine, Maxwell Logic 03E35 (Primary), 03E55 (Secondary) We introduce a forcing that adds a $\square(\aleph_2,\aleph_0)$-sequence with countable conditions under CH. Assuming the consistency of a weakly compact cardinal, we can find a forcing extension by our new poset in which both $\square(\aleph_2,<\!\aleph_0)$ and $\square_{\aleph_1,\aleph_0}$ fail in the forcing extension. |
| title | Unthreadability with Small Conditions |
| topic | Logic 03E35 (Primary), 03E55 (Secondary) |
| url | https://arxiv.org/abs/2209.12258 |