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.
Other articles related to "interpretation":
... The partial map f from Z —Z onto Q which maps x,y)to x/y provides an interpretationof the field Q of rational numbers in the ring Z of integers to be precise,the interpretationis 2,f) ... In fact,this particular interpretationis 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 ...