Model companions of taut for stable t

Abstract

We introduce the notion T does not omit obstructions. If a stable theory does not admit obstructions then it does not have the finite cover property (nfcp). For any theory T, form a new theory TAut by adding a new unary function symbol and axioms asserting it is an automorphism. The main result of the paper asserts the following: If T is a stable theory, T does not admit obstructions if and only if TAut has a model companion. The proof involves some interesting new consequences of the nfcp. © 2003 University of Notre Dame. All rights reserved.