Interpretation (model Theory)

Interpretation (model Theory)

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.