February 28
Andreas Lietz,
TU Wien
Equiconsistencies involving strengthenings of PFA
We discuss the famous open problem of determining the exact consistency strength of PFA. We present an equiconsistency between Ben Goodman's Sigma_n-Correct Proper Forcing Axiom, which implies PFA, and supercompact for C^(n-1)-cardinals under additional mild assumptions for large enough n. Without these assumptions we can prove a dichotomy resembling Woodin's HOD dichotomy with a model containing the mantle taking on the role of HOD.