The Classification of Small Types of Rank Ω , Part I
نویسندگان
چکیده
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 prove Theorem A. Let G be a superstable group of U− rank ω such that the generics of G are locally modular and Th(G) has few countable models. Let G be the group of nongeneric elements of G , G = Go + G . Let Π = {q ∈ S(∅) : U(q ↾ ∅) < ω } . For any countable model M of Th(G) there is a finite A ⊂ M such that M is almost atomic over A∪G(M)∪ ⋃ p∈Π p(M) .
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