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