Derived Models in PFA
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866911062841884672 |
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| author | Levinson, Derek Trang, Nam |
| author_facet | Levinson, Derek Trang, Nam |
| contents | We discuss a conjecture of Wilson that under the proper forcing axiom, $Θ_0$ of the derived model at $κ$ is below $κ^+$. We prove the conjecture holds for the old derived model. Assuming mouse capturing in the new derived model, the conjecture holds there as well. We also show $Θ< κ^+$ in the case of the old derived model, and under additional hypotheses for the new derived model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_05954 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Derived Models in PFA Levinson, Derek Trang, Nam Logic 03E45 (Primary) 03E60 Secondary We discuss a conjecture of Wilson that under the proper forcing axiom, $Θ_0$ of the derived model at $κ$ is below $κ^+$. We prove the conjecture holds for the old derived model. Assuming mouse capturing in the new derived model, the conjecture holds there as well. We also show $Θ< κ^+$ in the case of the old derived model, and under additional hypotheses for the new derived model. |
| title | Derived Models in PFA |
| topic | Logic 03E45 (Primary) 03E60 Secondary |
| url | https://arxiv.org/abs/2501.05954 |