A cardinal $\kappa$ is a *PFA cardinal* if $\kappa$ is not zero and
the canonical forcing of the PFA of length $\kappa$, which is the
countable support iteration that at each stage $\gamma$ forces with the
lottery sum of all minimal-rank proper partial orders $\mathbb{Q}$ for
which there is a family $\cal{D}$ of $\omega_1$ many dense sets in
$\mathbb{Q}$ for which there is no filter in $\mathbb{Q}$ meeting
them, forces PFA.
Every supercompact cardinal is a PFA cardinal. It is not yet clear
whether the converse is true.
Viale and Weiß have shown that an inaccessible PFA cardinal $\kappa$
for which the canonical forcing of the PFA makes $\kappa$ become
$\omega_2$ is
supercompact. {% cite Viale2011 %}