Martin's Maximum and the $\text{P}{}_{\mathrm{<mtext>max</mtext>}}\text{axiom}\text{(∗)}$

Abstract

Assuming the existence of a supercompact limit of supercompact cardinals, we modify the original consistency proof of Martin's Maximum to obtain a model in which MM holds but the $\text{P}{}_{\mathrm{<mtext>max</mtext>}}$ axiom $\text{(∗)}$ fails.