No subject
Dave Marker
marker at math.uic.edu
Wed Feb 13 18:38:44 EST 2002
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.
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