Pure computable model theory. (English) Zbl 0952.03037

Harizanov, Valentina S.

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)

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