On atomic or saturated sets

Journal of Symbolic Logic 61 (1):318-333 (1996)
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Assume T is stable, small and Φ(x) is a formula of L(T). We study the impact on $T\lceil\Phi$ of naming finitely many elements of a model of T. We consider the cases of $T\lceil\Phi$ which is ω-stable or superstable of finite rank. In these cases we prove that if T has $ countable models and Q = Φ(M) is countable and atomic or saturated, then any good type in S(Q) is τ-stable. If $T\lceil\Phi$ is ω-stable and (bounded, 1-based or of finite rank) with $I(T, \aleph_0) , then we prove that every good p ∈ S(Q) is τ-stable for any countable Q. The proofs of these results lead to several new properties of small stable theories, particularly of types of finite weight in such theories



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Non-isolated types in stable theories.Predrag Tanović - 2007 - Annals of Pure and Applied Logic 145 (1):1-15.

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References found in this work

Meager forking.Ludomir Newelski - 1994 - Annals of Pure and Applied Logic 70 (2):141-175.
Forking, normalization and canonical bases.Anand Pillay - 1986 - Annals of Pure and Applied Logic 32:61-81.
Fundamentals of Stability Theory.Anand Pillay - 1990 - Studia Logica 49 (4):608-609.

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