Computable model theory
Computable model theory is a branch of model theory which deals with questions of computability as they apply to model-theoretical structures.
History
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.
Introduction
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 model-theoretic conditions can be shown to exist.
gollark: You "can" break rules quite frequently. That doesn't mean it's sensible to.
gollark: Probably not people who violate ALL rules, but ones who violate *some subset* of them in interesting ways.
gollark: If you go out of your way to do exactly the opposite of what "rules" say, they have as much control over you as they do on someone who does exactly what the rules *do* say.
gollark: I'm glad you're making sure to violate norms in socially approved ways which signify you as "out there" or something.
gollark: > if you can convince them that their suffering benefits other people, then they'll happily submit to itI am not convinced that this is actually true of people, given any instance of "selfishness" etc. ever.
See also
References
- Harizanov, V. S. (1998), "Pure Computable Model Theory", in Ershov, Iurii Leonidovich (ed.), Handbook of Recursive Mathematics, Volume 1: Recursive Model Theory, Studies in Logic and the Foundations of Mathematics, 138, North Holland, pp. 3–114, ISBN 978-0-444-50003-8, MR 1673621.
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