On the number of non-almost isomorphic models ofTin a power
Saharon Shelah · Pacific Journal of Mathematics · 1971
Let T be a first order theory.Two models are almost isomorphic if they are elementarily equivalent in the language Loo, ω .We investigate the number of non almost-isomorphic models of T of power 2 as a function of λ, I(T, λ).We prove μ > λ ^ I TI, 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).