FOM: generic absoluteness and CH wtait at
Fri Dec 19 23:53:11 EST 1997

Please continue; but let me ask a question. You write (I'm not sure how this transmits, so: Steel writes) 
>However, the consistency strength order on large cardinal axioms
>corresponds to the inclusion order on their canonical minimal models. One
>can abstract certain very basic properties of a canonical inner model
>construction (roughly, one demands that it relativise to a real, and that
>the model M(x) built over the real x have a wellorder uniformly definable
>from x).
I realize that you are speaking about CH, which singles out the reals. But in discussing the question of its eventual decidability, we should be thinking of _general_ criteria for axioms of set theory. So why should relativization to a real x, the model M(x) Š etc., be what is decisive? Why should the reals, aside from historical accident, so to speak, play this distinguished role in foundations?

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