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[Dave Marker]

In his post Wed, 13 Feb 2002 10:26:35 -0500 

Harvey writes:

>9. WHAT IS THE RELATIONSHIP BETWEEN AN EXPANSION OF THE FIELD OF REALS
>BEING "TAME" AND IT HAVING AN EXPLICIT PROPER ELEMENTARY EXTENSION?

and in a later post remarks that o-minimal expansions of the reals
have canonical elementary extensions (namely germs at infinity
of definable functions).

In fact this is two somewhat different manifestations of "tameness".

First, in o-minimal structures all infinite elements realize the same
type.

Second, o-minimal expansions of an ordered group have definable
Skolem functions (or more generally o-minimal theories have prime
models over sets).

I suppose that in order to have an "explicit" elementary extension
one would first need to specify a canonical set of types to
be realized in the extenstion.