On 9 Dez., 17:24, fom <fomJ...@nyms.net> wrote: > 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 least in principle, shall be well-ordered, this > > nameability is crucial. > > > Indeed > > So, why is there no global axiom of choice?
As far as I am informed, *the* axiom of choice is global. There is no exception. Zermelo proved: Every set can be well-ordered. > > The constructible universe can be well-ordered.
Without axiom, because for countable sets the axiom is not required. > > 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.
That is my opinion too. But we know (and noone disputes it, as far as I know) that the set of all names is countable.