Cardinality, saturation and finiteness (Q1364727)

The author uses some results of J. Keisler and M. Benda to investigate relations between such properties of a model as its cardinality and saturation. Let \( {\mathcal M}\) be a model and \( ^{\ast}{ }{\mathcal M} \) be an extension of \({\mathcal M}\). Consistency of ZFC is supposed. Let be \( M\in{\mathcal M} \), \(\alpha\) be a cardinal. Denote by \(F_{\alpha}(M)\) the set of filters in \(M\). The set \(^{\ast}{ }M\) is said to be \({\alpha}\)-regular iff \({\forall}F{\in}F_{\alpha}(M)\:\:\)Monad\((F) \neq \emptyset\). Theorem 1 states that \(^{\ast}{ }M\) is \({\alpha}\)-regular iff \({\alpha}\) belongs to a hyperfinite internal set. The author mentions in the preface Theorem 2 but this is missing in the paper.