The **Proper Forcing Axiom** kills CH in a particularly specific way: it implies that $2^{\aleph_0}=\aleph_2$. However, its impact on the continuum function above $\aleph_0$ is much less clear. It is known, for example, that it implies the *Singular Cardinal Hypothesis*, SCH.

In this paper (see page 2), Aspero writes that Magidor showed the following:

Any model of ZFC+PFA has a forcing extension satisfying ZFC+PFA+"$2^\kappa=\kappa^+$ for all uncountable $\kappa$".

However, he does not give a reference; the bibliography mentions a set of (unpublished) lectures by Magidor. Googling around, I haven't found anything more specific.

I was wondering whether a proof of this exists in the literature, or - failing that - if someone could sketch an outline of it.