Harizanov, Valentina S. Pure computable model theory. (English) Zbl 0952.03037 Ershov, Yu. L. (ed.) et al., Handbook of recursive mathematics. Vol. 1: Recursive model theory. Amsterdam: Elsevier. Stud. Logic Found. Math. 138, 3-114 (1998). Model-theoretic notions and theorems are discussed from the point of view of computability theory. The author deals with effective omitting types theorem; decidable theories with decidable prime models, with decidable saturated and with decidable homogeneous models; decidable theories with only finitely many and with only countably many, non-isomorphic countable models; indiscernibles. A survey of the computability-theoretic and model-theoretic background is given, thus making the exposition self-contained.For the entire collection see [Zbl 0905.03001]. Reviewer: A.Ryaskin (Novosibirsk) Cited in 33 Documents MSC: 03C57 Computable structure theory, computable model theory 03D45 Theory of numerations, effectively presented structures 03C15 Model theory of denumerable and separable structures 03-02 Research exposition (monographs, survey articles) pertaining to mathematical logic and foundations 03C50 Models with special properties (saturated, rigid, etc.) Keywords:effective omitting types theorem; decidable theory; decidable prime model; decidable saturated model; decidable homogeneous model; countable model; indiscernibles; survey PDF BibTeX XML Cite \textit{V. S. Harizanov}, Stud. Logic Found. Math. 138, 3--114 (1998; Zbl 0952.03037)