Proper cuts in \(^*R\) (Q1364714)

The paper deals with various methods of constructing nonstandard models in which \(^{\ast}{ }R\) is Scott complete as well as models in which it is incomplete. The paper includes methods of S. Kamo, M. Forti and F. Honsell, H. J. Keisler and J. H. Schmerl [\textit{H. J. Keisler} and \textit{J. H. Schmerl}, ``Making the hyperreal line both saturated and complete'', J. Symb. Logic 56, No. 3, 1016-1025 (1991; Zbl 0747.03032)]. An ordered field \(K\) is called Scott complete if for every cut \((X,Y)\) in \(K\) such that \[ {\forall} {\epsilon{\in K}}{\:}({\epsilon}>0){\:}{\exists x}{\in X} {\:}{\exists y}{\in Y}{\:}(y-x{<\epsilon}) \] there exists a maximal element in \(X\) or a minimal element in \(Y\).