FOM: generic absoluteness and CH
wtait@ix.netcom.com
wtait at ix.netcom.com
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) etc., be what is decisive? Why should the reals, aside from historical accident, so to speak, play this distinguished role in foundations?
More information about the FOM
mailing list