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Topic Archive: model companion

Model theory seminarFriday, March 6, 201512:30 pmGC 6417

Alf Dolich

Generic Linear Functions over Divisible Ordered Abelian Groups

The City University of New York

Let T be the theory of divisible ordered Abelian groups in a language L
where T has quantifier elimination. Let f be a new unary function symbol. We
would like to consider the L(f)-theory T(a) expanding T together with axioms
for “f is an automorphism”. Unfortunately it is well known that T(a) does not
have a model companion and generally is not easy to analyze. Rather we look at
a weaker theory T(l) once again expanding T but with axioms for “l is a linear
bijection”. T(l) has a model companion and we provide a detailed analysis of
this theory.