On 12/9/2012 3:20 AM, WM wrote: > On 9 Dez., 08:21, fom <fomJ...@nyms.net> wrote: > > A hint: If you want to be read, write shorter. > >> In a footnote of his paper describing >> the constructible universe, Goedel makes >> it clear that the construction presupposes >> that every domain element can be named. > > For every set that, at leat in principle, shall be well-ordered, this > nameability is crucial. > > Regards, WM >
So, why is there no global axiom of choice?
The constructible universe can be well-ordered.
But, when people say they have obtained some models by forcing, that is just to say that an assumption of partiality demonstrated an element outside the ground model. Circular.
If those models cannot be put in correspondence with ORD should they not be considered meaningless?
It is the same question as that of accepting a completed infinity, although it is now in the realm of the transfinite. A "model" is a possible universe, and therby is a completion of sorts. But, nameability of elements is relevant.