An Iteration Theorem for $ω_1$-preserving Forcings
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913264501260288 |
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| author | Lietz, Andreas |
| author_facet | Lietz, Andreas |
| contents | We prove an iteration theorem which guarantees for a wide class of nice iterations of $ω_1$-preserving forcings that $ω_1$ is not collapse, at the price of needing large cardinals to burn as fuel. More precisely, we show that a nice iteration of $ω_1$-preserving forcings which force SRP at successor steps and preserves old stationary sets does not collapse $ω_1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_09018 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An Iteration Theorem for $ω_1$-preserving Forcings Lietz, Andreas Logic 03E35 03E55 03E57 We prove an iteration theorem which guarantees for a wide class of nice iterations of $ω_1$-preserving forcings that $ω_1$ is not collapse, at the price of needing large cardinals to burn as fuel. More precisely, we show that a nice iteration of $ω_1$-preserving forcings which force SRP at successor steps and preserves old stationary sets does not collapse $ω_1$. |
| title | An Iteration Theorem for $ω_1$-preserving Forcings |
| topic | Logic 03E35 03E55 03E57 |
| url | https://arxiv.org/abs/2403.09018 |