[FOM] Query on "smallness" bounds on 2^{\aleph_0} with all sets measurable

[todunion@ucollege.edu]

Is anyone aware of a known minimum value (or large cardinal property)
for how small the continuum could possibly be yet still have "all
sets Lebesgue measurable"?  (I think {\aleph_1} is automatically
ruled out, but just to be on the safe side, let me add: assuming ZFC
and not-CH)

I know there are results of Solovay linking consistency of measurable
cardinals with existence of a (non translation invariant of course)
extension of Lebesgue measure to all subsets of [0,1]; and that
(axiom):"2^{\aleph_0} is RVM" is equiconsistent with such an extension.

Tom Dunion
duniont_at_aol.com