Martin's Maximum${}^{\ast, ++}_{\mathfrak{c}}$ in $\mathbb{P}_{\max}$ extensions of strong models of determinacy
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911845891178496 |
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| author | Schindler, Ralf Yasuda, Taichi |
| author_facet | Schindler, Ralf Yasuda, Taichi |
| contents | We study a strengthening of $\mathrm{MM}^{++}$ which is called $\mathrm{MM}^{\ast, ++}$ and which was introduced by Asperó and Schindler. We force its bounded version $\mathrm{MM}^{\ast, ++}_{\mathfrak{c}}$, which is stronger than both $\mathrm{MM}^{++}(\mathfrak{c})$ as well as $\mathrm{BMM}^{++}$, by $\mathbb{P}_{\max}$ forcing over a determinacy model $L^{F_{\mathrm{uB}}}({\mathbb R}^*,\mbox{Hom}^{\ast})$. The construction of the ground model $L^{F_{\mathrm{uB}}}({\mathbb R}^{\ast},\mbox{Hom}^{\ast})$ builds upon Gappo and Sargsyan, and the derived model construction of Larson, Sargsyan, and Wilson. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_12836 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Martin's Maximum${}^{\ast, ++}_{\mathfrak{c}}$ in $\mathbb{P}_{\max}$ extensions of strong models of determinacy Schindler, Ralf Yasuda, Taichi Logic We study a strengthening of $\mathrm{MM}^{++}$ which is called $\mathrm{MM}^{\ast, ++}$ and which was introduced by Asperó and Schindler. We force its bounded version $\mathrm{MM}^{\ast, ++}_{\mathfrak{c}}$, which is stronger than both $\mathrm{MM}^{++}(\mathfrak{c})$ as well as $\mathrm{BMM}^{++}$, by $\mathbb{P}_{\max}$ forcing over a determinacy model $L^{F_{\mathrm{uB}}}({\mathbb R}^*,\mbox{Hom}^{\ast})$. The construction of the ground model $L^{F_{\mathrm{uB}}}({\mathbb R}^{\ast},\mbox{Hom}^{\ast})$ builds upon Gappo and Sargsyan, and the derived model construction of Larson, Sargsyan, and Wilson. |
| title | Martin's Maximum${}^{\ast, ++}_{\mathfrak{c}}$ in $\mathbb{P}_{\max}$ extensions of strong models of determinacy |
| topic | Logic |
| url | https://arxiv.org/abs/2404.12836 |