 For each sentence \(\phi\) of \(\mathbf{ZFC}\), there is another sentence \(\phi^* = (\exists f_1)\ldots(\exists f_n)\psi^*\) of \(\mathbf{ZFC}\) which says, intuitively, that ‘Skolem functions’ for \(\phi\) exist. These ‘Skolem functions’ are certain individuals of the domain of a model of \(\mathbf{ZFC}\). Here both \(\phi^*\) and \(\phi\) are first-order sentences. But if for every sentence \(\phi\) of \(\mathbf{ZFC}\) we have \(\phi\) and \(\phi^*\) being logically equivalent, why could the sentences \(\phi^*\) not be used for formulating a truth-predicate for \(\mathbf{ZFC}\) in \(\mathbf{ZFC}\) itself? However, by Tarski’s undefinability result, no such truth-predicate  exists.[78]  So there must be a model of \(\mathbf{ZFC}\) and a sentence \(\phi\) true in that model such that \(\phi^*\) is false: not all ‘Skolem functions’ asserted to exist by \(\phi^*\) actually exist in the model. 