[FOM] Model theory and foundations

[Alasdair Urquhart]

I'd like to addd a small observation to the debate
between John Baldwin, Steve Simpson and Harvey Friedman.
Nonstandard analysis is of clear foundational interest
and relevance, and unequivocally has its roots in
model theory.  

A surprising thing about nonstandard analysis is that
it exploits only very elementary model theory, 
specifically compactness and ultraproducts.  This leads
me to wonder just what foundational ideas we might
not discover by exploiting the great sophistication
of recent model theory.  

Incidentally, a recent article that I found interesting
that discusses the "foundational" aspects of model theory
is the piece by Angus Macintyre in the most recent issue
of the BSL (June 2003).  The basic theme of the piece
is that model theory is moving away from the Tarski 
paradigm towards a more geometrical inspiration.