Re: A question on GIT.

From: Herman Jurjus (h.jurjus_at_hetnet.nl)
Date: 09/10/04 

Date: Fri, 10 Sep 2004 07:56:44 +0200

peter_douglass wrote:

> "Herman Jurjus" <h.jurjus@hetnet.nl> wrote in message
> news:2qbpsuFsgsjpU1@uni-berlin.de...
>
>>peter_douglass wrote:
>
>
>>>What do you mean by "the only models of your theory would
>>>be non-standard?" What do you mean by non-standard numbers?
>
>
>>There exist models of PA (or Presburger Arithmetic, for that matter)
>>that contain an element x such that
>> 0 < x, 1 < x, 2 < x, etc.
>>This is a consequence of what one calls the 'compactness theorem' for
>>first order predicate logic.
>>Such 'unintended' models of PA are called non-standard, and x's having
>>that property are called non-standard.
>
>
> OK, that explains what you mean by non-standard, i.e. that there
> exists elements which are not in the standard model. Given that
> definition, is it true that the only models would be non-standard?
> I would think that any model of PA would also be a model of
> Presburger Arithmetic, given what I think you mean by model.

If PA is inconsistent and Presburger is not, then ... ? 

-- 
Cheers,
Herman Jurjus

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