I see the importance you are attaching to your Ultimate L Conjecture — particularly getting a proof “by the current scenarios of course”. Care to make rough probabilistic predictions on when you will prove it “by the current scenarios of course”? Until then, your point of view seems to be that statements like Con(HUGE) are wide open, and you currently are not willing to declare any confidence in them.

Fascinating as this is, I think people here might be even more interested in the implications Con(EFA) arrows Con(PA) arrows Con(Z) arrows Con(ZFC) arrows Con(ZFC + measurable) arrows Con(ZFC + PD). Maybe you can comment on at least one of these arrows? — or maybe Peter Koellner?

Harvey