Date: Dec 9, 2012 1:30 PM
Subject: Re: fom - 01 - preface
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.
> 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.