  where \(\dom(f)\) is the domain of function \(f\) and \(\range(f)\) is the range of function \(f\). The \(B\)-valued universe is the proper class \(V(B)\) which is the union of all of these \(V\)s. Next, one defines by a rather complicated transfinite recursion over well-founded sets the value of a set-theoretic formula with elements of the Boolean valued universe assigned to its free variables: