MODEL COMPANIONS OF THEORIES WITH AN AUTOMORPHISM

KIKYO HIROTAKA

Abstract. For a theory T in L, T_{σ} is the theory of the models of T with an automorphism σ. If T is an unstable model complete theory without the independence property, then T_{σ} has no model companion. If T is an unstable model complete theory and T_{σ} has the amalgamation property, then T_{σ} has no model companion. If T is model complete and has the fcp, then T_{σ} has no model completion.