In model theory, interpretation of a structure M in another structure N (typically of a different signature) is a technical notion that approximates the idea of representing M inside N. For example, every reduct or definitional expansion of a structure N has an interpretation in N.
Many model-theoretic properties are preserved under interpretability. For example, if the theory of N is stable and M is interpretable in N, then the theory of M is also stable.
Note that in other areas of mathematical logic, the term "interpretation" may refer to a structure,[1][2] rather than being used in the sense defined here. These two notions of "interpretation" are related but nevertheless distinct.
- ^ Goldblatt, Robert (2006), "11.2 Formal Language and Semantics", Topoi : the categorial analysis of logic (2nd ed.), Mineola, N.Y.: Dover Publications, ISBN 978-0-486-31796-0, OCLC 853624133
- ^ Hodges, Wilfrid (2009), "Functional Modelling and Mathematical Models", in Meijers, Anthonie (ed.), Philosophy of technology and engineering sciences, Handbook of the Philosophy of Science, vol. 9, Elsevier, ISBN 978-0-444-51667-1