 For each node \(k\) let \(L(k)\) be the language extending \(L\) by new constants for all the elements of \(D(k).\) To each node \(k\) and each \(0\)-ary predicate letter (each proposition letter) \(P,\) either assign \(f(P, k) =\) true or leave \(f(P, k)\) undefined, consistent with the requirement that if \(k \le k'\) and \(f(P, k) =\) true then \(f(P, k') =\) true also. Say that: