# Blog Archives

# Topic Archive: model companion

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

# 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.