**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.

Read more about Interpretation (model Theory): Definition, Bi-interpretability, Example

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Interpretation (model Theory) - Example

... The partial map f from Z —Z onto Q which maps x,y)to x/y provides an

... The partial map f from Z —Z onto Q which maps x,y)to x/y provides an

**interpretation**of the field Q of rational numbers in the ring Z of integers to be precise,the**interpretation**is 2,f) ... In fact,this particular**interpretation**is often used to define the rational numbers ... To see that it is an**interpretation**(without parameters) one needs to check the following preimages of definable sets in Q the preimage of Q is defined by the formula ...