Marginalia to a Theorem of Asperó and Schindler
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913616786096128 |
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| author | Kasum, Obrad Veličković, Boban |
| author_facet | Kasum, Obrad Veličković, Boban |
| contents | We give a game-theoretic characterization of when a model of an infinitary propositional formula can be added by a proper, semiproper, and stationary-set-preserving poset. In the latter case, we also give a general sufficient condition for the existence of such a poset. We use this condition to give a somewhat different proof of the theorem of Asperó and Schindler, which states that $\mathsf{MM}^{++}$ implies Woodin's axiom $(*)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_08293 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Marginalia to a Theorem of Asperó and Schindler Kasum, Obrad Veličković, Boban Logic 03E40 (Primary) 03E57, 03C75 (Secondary) We give a game-theoretic characterization of when a model of an infinitary propositional formula can be added by a proper, semiproper, and stationary-set-preserving poset. In the latter case, we also give a general sufficient condition for the existence of such a poset. We use this condition to give a somewhat different proof of the theorem of Asperó and Schindler, which states that $\mathsf{MM}^{++}$ implies Woodin's axiom $(*)$. |
| title | Marginalia to a Theorem of Asperó and Schindler |
| topic | Logic 03E40 (Primary) 03E57, 03C75 (Secondary) |
| url | https://arxiv.org/abs/2308.08293 |