# Maximal Automorphisms

## Alf Dolich

### The City University of New York

A maximal automorphism of a structure M is an automorphism under which no non-algebraic element of M is fixed. A problem which has attracted some attention is when for a theory T any countable recursively saturated model of T has a maximal automorphism. In this talk I will review what is known about this problem in various contexts and then prove a general result that guarantees, under certain mild conditions on T, that any countable recursively saturated model of T does indeed have a maximal automorphism.

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.