Let S be a non empty relational structure and let X be a set. We introduce X has the minimum in S as a synonym of min X exists in S . We introduce X has the maximum in S as a synonym of max X exists in S . Let S be a non empty relational structure, let s be an element of S , and let X be a set. Let L be a relational structure.
L is isomorphic.
There exists a map from L 1 into L 2 which is isomorphic. Let us note that the predicate L 1 and L 2 are isomorphic is reflexive. Suppose L 1 and L 2 are isomorphic and L 2 and L 3 are isomorphic. Then L 1 and L 3 are isomorphic.