fom
Posts:
1,032
Registered:
12/4/12
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Re: fom - 01 - preface
Posted:
Dec 9, 2012 7:02 PM
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On 12/9/2012 12:30 PM, WM wrote:
> On 9 Dez., 17:24, fom <fomJ...@nyms.net> wrote:
>> On 12/9/2012 3:20 AM, WM wrote:
<snip>
>> 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 axiom of choice only applies to sets within
a given model.
Consequently, for any set model whose domain is
obtained from a larger model, the axiom of
choice holds from the larger model.
But, the constructible universe is a class model.
Models obtained from the constructible universe
by forcing methods need not have a one-to-one
correspondence with the ordinals as defined in
their scope. The axiom of choice only applies
to the objects of the domain.
My question speaks to what may be considered
as admissible as a model in such cases.
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