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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.12836 |
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Table of 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.