Abstract

We prove Theorem A.Every resplendent model of an ω-stable theory is homogeneous. As an application we obtain Theorem B.Suppose T is ω-stable, M ⊨ T is recursively saturated and P ∈ S (M) is such that for all finite\(\bar m\) ∈ M, p ↑\(\bar m\) is realized in M. Then there is a\(\bar c\) ∈ M and a definition d of p over\(\bar c\) such that d is recursive in t (\(\bar c\)/O).

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