 Given an L-structure \(\mm\), an assignment is a function s from variables to the domain M of \(\mm\) such that: if x is an individual variable, then \(s(x) \in M\); if X is relation variable of arity n, then \(s(X) \subseteq M^n\); if F is function variable of arity n, then \(s(F) : M^n \to M\). We use \(s(P/X)\) to denote the assignment which is otherwise as s except that the value at X has been changed to P. Similarly \(s(a/x)\) and \(s(f/F)\).