Re: A question on GIT.

From: peter_douglass (baisly_at_gis.net)
Date: 09/10/04 

Date: Fri, 10 Sep 2004 02:15:52 GMT

"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.
The axioms of PA are a superset of the axioms of Presburger
Arithmetic, so I would believe that any model of PA would also
be a model of the weakened theory. But perhaps I misunderstand
something.

--PeterD

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