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Article #5654

Re: Lowenheim-Skolem theorem (was: Continuos vs. discrete models)

#5654
From: rivero
Date: Thu, 19 Nov 1992 17:28
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In article <COLUMBUS.92Nov19105153@strident.think.com> Michael Weiss,
columbus@strident.think.com writes:
>Assuming one could axiomatize, say, QED as a consistent first-order theory
>(insert obligatory comment by John Baez on how this hasn't been done yet--
>that is, the combination of defining the formal system QED and proving
>Con(ZF)-->Con(QED) hasn't been carried out), it follows that there is a
>countable model that looks EXACTLY LIKE the continous model, so far as
>statements we can make in the language of the theory.  And if the
>axiomatization is worthy of the name, then such statements are all a
>physicist cares about.  Metamathematics is metaphysics, in this case.


Wasnt L-H theorem the kind of things that let you go in both directions?
This is, given a model, you can get ones with lower cardinality, and
others with higher. 
I think to remember that you can always go higher by using 
Los theorem, ultraproducts, or something so?. This was the thing
Robinson did to go over no-standard (*), is this? 
 
(Sorry by the quantity of question marks, but Metamatematical Physics
is always a peripherical issue)

-Alejandro Rivero
Zaragoza Univ, Spain

(*) In this sense ,there was some papers from S. Albeverio relating
non standard constructions and path integral integrations etc...
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From: rivero <rivero@cc.unizar.es>
Subject: Re: Lowenheim-Skolem theorem (was: Continuos vs. discrete models)
Message-ID: <1992Nov19.172844.17787@ulrik.uio.no>
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References: <1992Nov17.124233.24312@oracorp.com> <361@mtnmath.UUCP> <TORKEL.92Nov18193457@bast.sics.se> <COLUMBUS.92Nov19105153@strident.think.com>
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