Second-order-arithmetic augmented with the axioms of projective determinacy seems to be quite a strong theory.
Does this system proof the consistency of ZFC or better ZFC + some large cardinals?
2026-05-05 09:39:28.1777973968
Does second-order-arithmetic + PD proof consistency of ZFC?
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Yes, second-order arithmetic plus PD proves the consistency of ZFC plus a good supply of large cardinals. If I remember correctly, it's equiconsistent with ZFC plus the existence of $n$ Woodin cardinals for all (really) finite $n$.