Amirkabir University of Technology AUT Journal of Mathematics and Computing 2783-2449 3 1 2022 02 01 An effective version of definability in metric structures 101 111 4645 10.22060/ajmc.2021.20660.1071 EN Nazanin Roshandel Tavana Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran Journal Article 2021 10 12 In this paper, a computably definable predicate in metric structures is defined and characterized. Then, it is proved that every separable infinite-dimensional Hilbert structure in an effectively presented language is computable. Moreover, every definable predicate in these structures is computable. metric model theory TTE https://ajmc.aut.ac.ir/article_4645_b831289d99a122a648db55e2469b565f.pdf