The proper forcing axiom and stationary set reflection (Q1262859)

Our main result is that the proper forcing axiom (PFA) is equiconsistent with ``PFA \(+\) there is a nonreflecting stationary subset of \(\omega_ 2''\). More generally we show for any cardinals \(n<m\leq \aleph_ 2\) that if \(PFA^+(n)\) is consistent with ZFC then so is \(``PFA^+(n)\) \(+\) there are m mutually nonreflecting stationary subsets of \(\omega_ 2''\). As corollaries it follows that if \(n<m\leq \aleph_ 1\) then \(PFA^+(n)\) (if consistent) does not imply \(PFA^+(m)\), and that PFA (if consistent) does not imply Martin's maximum.