On the number of non-almost isomorphic models of t in a power

Let T be a first order theory. Two models are almost isomorphic if they are elementarily equivalent in the language L_∞,ω. We investigate the number of non almost-isomorphic models of T of power λ as a function of λ, I(T, λ). We prove µ > λ ≧ |T|, I(T, λ ≦ λ implies I(T, µ) ≦ I(T,λ). In fact, we generalize the downward Skolem-Lowenheim theorem for infinitary languages. Th. (1, 4, 5).