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Martin's Maximum${}^{\ast, ++}_{\mathfrak{c}}$ in $\mathbb{P}_{\max}$ extensions of strong models of determinacy
- Publication Year :
- 2024
-
Abstract
- We study a strengthening of $\mathrm{MM}^{++}$ which is called $\mathrm{MM}^{\ast, ++}$ and which was introduced by Asper\'o 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.
- Subjects :
- Mathematics - Logic
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2404.12836
- Document Type :
- Working Paper