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Topic: fom - 01 - preface
Replies: 35   Last Post: Dec 16, 2012 12:20 AM

 Messages: [ Previous | Next ]
 fom Posts: 1,968 Registered: 12/4/12
Re: fom - 01 - preface
Posted: Dec 10, 2012 10:55 PM

On 12/10/2012 2:43 PM, Virgil wrote:
> In article
> WM <mueckenh@rz.fh-augsburg.de> wrote:
>

>> On 10 Dez., 01:02, fom <fomJ...@nyms.net> wrote:
>>> 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.

>>
>> Zermelo proved that every set can be well-ordered - without mentioning
>> any model. My interest is solely the set of real numbers. It is
>> covered by Zermelo's proof.

>
> Does WM claim that Zermelo's "proof" must hold in every model, that it
> is somehow universal?

Well, it certainly holds whenever the theory
being modeled has the axoim of choice.

I wonder how the claim holds when the axiom
of determinacy is in force and the axiom of
choice is inconsistent.

I suppose, that the claim is interpretable along
the lines of finitism. Completeness is of no
issue. What can be proved using a sound deductive
system is what is true. Then the only real numbers
are the constructive real numbers.

Date Subject Author
12/7/12 fom
12/8/12 Zaljohar@gmail.com
12/8/12 mueckenh@rz.fh-augsburg.de
12/8/12 fom
12/8/12 mueckenh@rz.fh-augsburg.de
12/8/12 Virgil
12/9/12 mueckenh@rz.fh-augsburg.de
12/9/12 Virgil
12/8/12 fom
12/8/12 ross.finlayson@gmail.com
12/9/12 fom
12/9/12 mueckenh@rz.fh-augsburg.de
12/9/12 fom
12/9/12 mueckenh@rz.fh-augsburg.de
12/9/12 fom
12/10/12 mueckenh@rz.fh-augsburg.de
12/10/12 Virgil
12/10/12 fom
12/10/12 ross.finlayson@gmail.com
12/11/12 fom
12/12/12 ross.finlayson@gmail.com
12/12/12 Virgil
12/16/12
12/9/12 ross.finlayson@gmail.com
12/9/12 fom
12/9/12 ross.finlayson@gmail.com
12/9/12
12/10/12 fom
12/9/12 mueckenh@rz.fh-augsburg.de
12/8/12 Virgil
12/9/12 mueckenh@rz.fh-augsburg.de
12/9/12 Virgil
12/9/12 Zaljohar@gmail.com
12/9/12 mueckenh@rz.fh-augsburg.de
12/10/12 Dan Christensen
12/11/12 fom