I need some quick help...
I got a presentation on Thursday about how one can use forcing to prove the independence of the continuum hypothesis (the independence from ZFC....)
So, using forcing to prove Con(ZFC) ==> Con(ZFC + ~CH) is pretty easy...
but....
all the proofs I can find of Con(ZFC) ==> Con(ZFC + CH) which use forcing are more complicated than I'd like to get. In fact, all of them I've found are Con(ZFC) ==> Con(ZFC + diamond), which leads to a prove of the consistency of the generalized continuum hypothesis. I don't need a proof of the consistency of GCH, just one of CH, using forcing.
I suppose I could always resort to Godel's method from 1940, it's just that, knowing a method exists using forcing, I'd like to find a way to simplify it.
Thanks
PS, sorry for those of you who are part of several math communities, don't mean to double/triple/quadruple post...