sorry for reposting this, if you replied to it in the meantime. I don't want to have people more confused with half-finished sentences
>>11629716>>11629730I can't tell who's who but best not use my P(n) as a set, I don't know why
>>11629716says
> bijection f between \omega_1 and P(N)or why
>>11629730says P isn't in the language of set theory.
Both of your claims seem wrong in that instances
>>11629704Well I'm not going to expands the definition of \omega_1 for you guys.
But let me see how far I can get with your or his (who ever of you is the "vacuuously true guy" Shyamalan rhetoric guys) claim.
I suppose it's
>>11629720Say w, r are two set variables and Ind(w) and U(r) say that w is the smallest inductive set and r is the first uncountable sets.
The idea, I understand, is to recast CH as
forall r, w. U(r) => [Ind(w) => ch(w, r)]
where little "ch" means
|w -> {0,1}| = |r|
where "=" is the existence claim of a bijection
So dissolving the implications under the forall as
P=>Q ... ]not P] or Q,
then CH is
forall r, w. [not U(r)] or [[not Ind(w)] or ch(w, r)]
i.e.
forall r, w. [not U(r)] or [not Ind(w)] or ch(w, r)]
and if we take the second disjunct as an axiom, we should be done.
done with simplifying anyway, tell me if that kind of formulation is what you wanted to get at or where the misinterpretation is
?
