A structure theorem for strongly abelian varieties with few models

By a variety, we mean a class of structures in some language containing only function symbols which is equationally defined or equivalently is closed under homomorphisms, submodels and products.If K is a class of -structures then I(K, λ) denotes the number of nonisomorphic models in K of cardinality λ. When we say that K has few models, we mean that I(K,λ) < 2λ for some λ > ∣∣. If I(K,λ) = 2λ for all λ > ∣∣, then we say K has many models. In [9] and [10], Shelah has shown that for an elementary class K, having few models is a strong structural condition.

A structure theorem for strongly abelian varieties with few models Journal Articles