Date: Dec 9, 2012 1:30 PM
Author: mueckenh@rz.fh-augsburg.de
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.

> >

> 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.

Regards, WM