Martin's maximum conjecture for forcing extensions of Hℵ2H_{\aleph_2}Hℵ2
Let VVV be a model of MM++{\text{{\sf MM}}}^{++}MM++ together with large cardinals, and let P∈VP\in VP∈V preserve MM++{\text{{\sf MM}}}^{++}MM++. Martin's maximum conjecture. For every such PPP, ……