 When a structure \(B\) is interpreted in a structure \(A\), every first-order statement about \(B\) can be translated back into a first-order statement about \(A\), and in this way we can read off the complete theory of \(B\) from that of \(A\). In fact if we carry out this construction not just for a single structure \(A\) but for a family of models of a theory \(T\), always using the same defining formulas, then the resulting structures will all be models of a theory \(T'\) that can be read off from \(T\) and the defining formulas. This gives a precise sense to the statement that the theory \(T'\) is interpreted in the theory \(T\). Philosophers of science have sometimes experimented with this notion of interpretation as a way of making precise what it means for one theory to be reducible to another. But realistic examples of reductions between scientific theories seem generally to be much subtler than this simple-minded model-theoretic idea will allow. See the entry on  intertheory relations in physics.