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On finitely generated models. (Russian) Zbl 0624.03026
A model of a countable first order theory is said to be finitely generated if it is prime over a finite set. A. Pillay [J. Symb. Logic 48, 163-166 (1983; Zbl 0519.03024)] proved that any countable model of an \(\omega\)-stable theory is the union of an elementary chain of finitely generated models. This result was obtained as a corollary of a more interesting theorem proved in the same paper. The author generalizes the result for theories having the property that for any finite set there is a prime model over it. The proof is easier than Pillay’s one, but the text contains some misprints.
Reviewer: A.N.Ryaskin

MSC:
03C15 Model theory of denumerable and separable structures
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