 An understanding of the distinction between standard and nonstandard models can clarify many phenomena. For example, it can be shown that there is a model \(\cM = \langle \{\cD_{\alpha}\}_{\alpha}, \frI\rangle\) in which \(\cD_{\imath}\) is infinite, and all the domains \(\cD_{\alpha}\) are countable. Thus \(\cD_{\imath}\) and \(\cD_{{o}\imath}\) are both countably infinite, so there must be a bijection h between them. However, Cantor’s Theorem (which is provable in type theory and therefore valid in all models) says that \(\cD_{\imath}\) has more subsets than members. This seemingly paradoxical situation is called Skolem’s Paradox. It can be resolved by looking carefully at Cantor’s Theorem, i.e., \(\nsim \exists g_{{o}\imath\imath}\forall f_{{o}\imath}\exists j_{\imath}[g_{{o}\imath\imath}j_{\imath} = f_{{o}\imath}]\), and considering what it means in a model. The theorem says that there is no function \(g \in \cD_{{o}\imath\imath}\) from \(\cD_{\imath}\) into \(\cD_{{o}\imath}\) which has every set \(f_{{o}\imath} \in \cD_{{o}\imath}\) in its range. The usual interpretation of the statement is that \(\cD_{{o}\imath}\) is bigger (in cardinality) than \(\cD_{\imath}\). However, what it actually means in this model is that h cannot be in \(\cD_{{o}\imath\imath}\). Of course, \(\cM\) must be nonstandard.