Abstract: 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.
Publication Year: 1996
Publication Date: 1996-03-01
Language: en
Type: article
Indexed In: ['crossref']
Access and Citation
Cited By Count: 6
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