On atomic or saturated sets
AbstractAssume 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.
1962 ◽
Vol 14
◽
pp. 169-257
◽
Keyword(s):
1997 ◽
Vol 161
◽
pp. 189-195
Keyword(s):
1970 ◽
Vol 28
◽
pp. 474-475
Keyword(s):
1996 ◽
Vol 54
◽
pp. 910-911
1996 ◽
Vol 54
◽
pp. 1034-1035