Prime extensions and categoricity in power

This paper deals with the notion of prime extension defined by Morley. A connection is established between the categoricity of a theory in a cardinal greater than the power of its language and the existence of prime extensions. For such theories we prove a minimality property of the prime extensions and we conclude by a property of the group of automorphisms of their models. Author working on Ph. D. thesis under supervision of Prof. M. O. Rabin. Author working at the CNRS under the supervision of Prof. D. Lacombe.