[FOM] The width of V
E. Todd Eisworth
eisworth at math.uni.edu
Wed Jul 9 14:32:26 EDT 2003
[Jones]
Can anyone point me to work on axioms which
are intended to make V as fat as possible?
[Kanovei]
Martin's axiom MA makes continuum rather fat because
it implies that holes of certain kind are fulfilled.
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>From Woodin's book "The Axiom of Determinacy, Forcing Axioms, and the
Nonstationary Ideal" (pg 9)
--- Begin Quote ---
These theorems suggest that the axiom:
(*) AD holds in L(R) and L(P(\omega_1)) is a P_max-generic extension of
L(R);
is perhaps, arguably, the correct maximal generalization of Martin's
Axiom at least as far as the structure of P(\omega_1) is concerned.
--- End Quote ---
The earlier axioms Martin's Maximum has the same spirit but different
execution --- the references are
Foreman, Magidor, and Shelah Martin's Maxium, saturated ideals, and
non-regular ultrafilters, Part I. Annals of Mathematics 127 (1988) 1-47.
Part II is in Annals of Mathematics 127 (1988) 521-545.
###########
By the way, I've had Woodin's book sitting on and around my desk for the
better part of four years. I've picked it up and read "just for fun" but
I've never tried to work through the material seriously because I didn't
think I had the required expertise in "California set theory".
Are there other set theorists out there in similar situations? Should we
pool resources and try to do something about it?
Todd
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