 Computable model theory

Computable model theory is a branch of model theory which deals with questions of computability as they apply to modeltheoretical structures. It was developed almost simultaneously by mathematicians in the West, primarily located in the United States and Australia, and Soviet Russia during the middle of the 20th century. Because of the Cold War there was little communication between these two groups and so a number of important results were discovered independently.
Computable model theory introduces the ideas of computable and decidable models and theories and one of the basic problems is discovering whether or not computable or decidable models fulfilling certain modeltheoretic conditions can be shown to exist.
References
 Harizanov, V. S. (1998), "Pure Computable Model Theory", in Ershov, Iurii Leonidovich, Handbook of Recursive Mathematics, Volume 1: Recursive Model Theory, Studies in Logic and the Foundations of Mathematics, 138, North Holland, pp. 3–114, ISBN 9780444500038, MR1673621.
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