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On atomic or saturated sets

Published online by Cambridge University Press:  12 March 2014

Ludomir Newelski
Ludomir Newelski*
Affiliation:
Impan, ul. Kopernika 18, 51-617 Wrocław, Poland, E-mail: newelski@math.uni.wroc.pl
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Abstract

Assume T is stable, small and Φ(x) is a formula of L(T). We study the impact on T⌈Φ of naming finitely many elements of a model of T. We consider the cases of T⌈Φ 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⌈Φ is ω-stable and (bounded, 1-based or of finite rank) with , 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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 61 , Issue 1 , March 1996 , pp. 318 - 333
Copyright
Copyright © Association for Symbolic Logic 1996

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References

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