Abstract

Abstract.Certain basic concepts of geometrical stability theory are generalized to a class of closure operators containing algebraic closure. A specific case of a generalized closure operator is developed which is relevant to Vaught's conjecture. As an application of the methods, we proveTheorem A.Let G be a superstate group of U-rankωsuch that the generics of G are locally modular andTh(G)has few countable models. Let G−be the group of nongeneric elements of G.G+=Go+G−.LetΠ = {q∈S(∅):U(q)<ω}.For any countable model M ofTh(G)there is a finite A⊂M such thai M is almost atomic over A∪ (G+∩M) ∪ ⋃p∈Πp(M).