Much stronger forcing axioms than MA were introduced in the 1980s, such as J. Baumgartner’s Proper Forcing Axiom (PFA), and the stronger Martin’s Maximum (MM) of Foreman, Magidor, and Shelah (1988), which is essentially the strongest possible forcing axiom. Both the PFA and MM are consistent relative to the existence of a supercompact cardinal. The PFA asserts the same as MA, but for partial orderings that have a property weaker than the ccc, called properness, introduced by Shelah. And MM asserts the same for the wider class of partial orderings that, when forcing with them, do not destroy stationary subsets of \(\omega_1\).