Di Nasso, Mauro; Forti, Marco On the ordering of the nonstandard real line. (English) Zbl 1016.03071 Zhang, Yi (ed.), Logic and algebra. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 302, 259-273 (2002). The order properties of the nonstandard real numbers have been investigated previously. In this paper, the authors, using a standard Robinson-styled superstructure approach, continue this investigation. For the hyperreals, they isolate the basic order-types, investigate order-isomorphisms between the infinitesimals, the infinite numbers and the entire hyperreal line. Further, they compute the main cardinal invariants for the order-topology of the hyperreals.For the entire collection see [Zbl 0994.00017]. Reviewer: Robert A.Herrmann (Annapolis) MSC: 03H05 Nonstandard models in mathematics 03C20 Ultraproducts and related constructions 06F30 Ordered topological structures Keywords:nonstandard analysis; hyperreals; order properties PDFBibTeX XMLCite \textit{M. Di Nasso} and \textit{M. Forti}, Contemp. Math. 302, 259--273 (2002; Zbl 1016.03071)