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Recently the second author introduced combinatorial principles thatcharacterize supercompactness for inaccessible cardinals but can also hold truefor small cardinals. We prove that the proper forcing axiom PFA implies theseprinciples hold for $\omega_2$. Using this, we argue to show that any of theknown methods for forcing models of PFA from a large cardinal assumptionrequires a strongly compact cardinal. If one forces PFA using a proper forcing,then we get the optimal result that a supercompact cardinal is necessary.

On the consistency strength of the proper forcing axiom