Martin's Maximum${}_{\mathfrak{c}}^{\ast ,++}$ in ${\mathbb{P}}_{\max }$ extensions of strong models of determinacy

Ralf Schindler, Taichi Yasuda

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}^…