Finite diagrams stable in power

In this article we define when a finite diagram of a model is stable, we investigate what is the form of the class of powers in which a finite diagram is stable, and we generalize some properties of totally transcendental theories to stable finite diagrams. Using these results we investigate several theories which have only homogeneous models in certain power. We also investigate when there exist models of a certain diagram which are λ-homogenous and not λ⁺-homogeneous in various powers. We also have new results about stable theories and the existence of maximally λ-saturated models of power μ.