  When mathematicians introduce a class of structures, they like to define what they count as the basic maps between these structures. The basic maps between structures of the same signature K are called homomorphisms, defined as follows. A homomorphism from structure A to structure B is a function f from dom(A) to dom(B) with the property that for every atomic formula φ(v1,…,vn) and any n-tuple a = (a1,…,an) of elements of A,