ABSTRACT

Introduction. Since the original works [39,40] by Abraham Robinson, many different presentations to the methods of nonstandard analysis have been proposed over the last forty years. The task of combining in a satisfactory manner rigorous theoretical foundations with an easily accessible exposition soon revealed very difficult to be accomplished. The first pioneering work in this direction was W.A.J. Luxemburg’s lecture notes [36]. Based on a direct use of the ultrapower construction, those notes were very popular in the “nonstandard” community in the sixties. Also Robinson himself gave a contribution to the sake of simplification, by reformulating his initial typetheoretic approach in a more familiar set-theoretic framework. Precisely, in his joint work with E. Zakon [42], he introduced the superstructure approach, by now the most used foundational framework.