On a Question of Hamkins and Löwe on the modal logic of collapse forcing
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2016
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| _version_ | 1866909247504121856 |
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| author | Golshani, Mohammad Mitchell, William |
| author_facet | Golshani, Mohammad Mitchell, William |
| contents | Hamkins and Löwe asked whether there can be a model $N$ of set theory with the property that $N\equiv N[g]$ whenever $g$ is a generic collapse of a cardinal of $N$ onto $ω$. We give equiconsistency results for two weaker versions of this property. We also include a proof of Woodin's result that the consistency of the full Hamkins-Löwe property follows from that of a Woodin cardinal with an inaccessible above. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1609_02633 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | On a Question of Hamkins and Löwe on the modal logic of collapse forcing Golshani, Mohammad Mitchell, William Logic Hamkins and Löwe asked whether there can be a model $N$ of set theory with the property that $N\equiv N[g]$ whenever $g$ is a generic collapse of a cardinal of $N$ onto $ω$. We give equiconsistency results for two weaker versions of this property. We also include a proof of Woodin's result that the consistency of the full Hamkins-Löwe property follows from that of a Woodin cardinal with an inaccessible above. |
| title | On a Question of Hamkins and Löwe on the modal logic of collapse forcing |
| topic | Logic |
| url | https://arxiv.org/abs/1609.02633 |