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Iterated extensions of models of countable theories and their applications. (English. Russian original) Zbl 0897.03033
Algebra Logic 34, No. 6, 346-358 (1995); translation from Algebra Logika 34, No. 6, 623-645 (1995).
The problem of determining the number of nonisomorphic countable models of a first order theory in a countable language has occupied a central place in classical model theory. The authors develop an approach to this problem based on iterated extensions of the language with new predicates associated to incomplete types. Among the applications, the authors give a new, direct proof of Morley’s theorem and the theorem about the finite type rank of an Ehrenfeucht theory which does not rely on descriptive set theory.

MSC:
03C45 Classification theory, stability, and related concepts in model theory
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