# Generic Linear Functions over Divisible Ordered Abelian Groups

## Alf Dolich

### 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.

Professor Dolich (Ph.D. 2002 University of Maryland, M.A. Columbia University, B.A. University of Pennsylvania) held a VIGRE Van Vleck Assistant Professorship at the University of Wisconsin, Madison, before coming to the New York area, where he now holds an Assistant Professor position at Kingsborough CC of CUNY. Professor Dolich conducts research in model theory, simple theories, and o-minimal theories with secondary interests in algebraic geometry and set theory.