An Introduction to Nonstandard Analysis

Abstract

Motivated by the historic concept of infinitesimals we treat the subject of nonstandard analysis. The present text is an introduction on the subject and takes a constructive approach. First we construct a nonstandard version of the reals in which we find the infinitesimals. Then using ultrafilters and ultraproducts, we generalise this method to construct a nonstandard version of any set. Finally we identify which nonstandard objects are pleasant to work with by giving them the label `internal’. The latter is done using superstructures.