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The classification of small types of rank ω, Part I
Published online by Cambridge University Press: 12 March 2014
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 prove
Theorem A. Let G be a superstate 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 thai M is almost atomic over A ∪ (G+ ∩ M) ∪ ⋃p∈Πp(M).
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- Copyright © Association for Symbolic Logic 2001