homomorphism in model theory, a structurepreserving mapping from one structure to another. A structure consists of a domain of objects together with a function specifying interpretations, with respect to that domain, of the relation symbols, function symbols, and individual symbols of a given language. Relations, functions, and individuals in different structures for a language L correspond to one another if they are interpretations of the same symbol of L. To call a mapping ‘structure-preserving’ is to say (1) that if objects in the first structure bear a certain relation to one another, then their images in the second structure (under the mapping) bear the corresponding relation to one another, (2) that the value of a function for a given object (or ntuple of objects) in the first structure has as its image under the mapping the value of the corresponding function for the image of the object (or n-tuple of images) in the second structure, and (3) that the image in the second structure of an object in the first is the corresponding object. An isomorphism is a homomorphism that is oneto-one and whose inverse is also a homomorphism. See also MODEL THEORY. R.Ke.