 On the other hand, in order for the Completeness Theorem to be applicable, a semantic argument has to be such that it works whatever model of set theory we are using. This means that a semantic argument in set theory should not use properties of individual models of set theory unless they are universal first order properties of all models of ZFC. In practice this means that if a property such as \(CH\), \(\Diamond\), \(2^{\aleph_0}=\aleph_2\), and so on, is used, it is mentioned separately as an assumption. Non-first order properties of models cannot be used at all, or else the Completeness Theorem cannot be used. Still, sometimes non-first order properties are used. For example, we may have an argument that every countable model of ZFC satisfies \(\phi\). But then, by the Downward Löwenheim-Skolem Theorem, every model of ZFC satisfies \(\phi\). Thus we have been able to eliminate the non-first order assumption of the countability of the model.