An application of non-standard model theoretic methods to topological groups and infinite Galois theory.

The purpose of this paper is to review some of the work done by Abraham Robinson in topological groups and infinite Galois Theory using ultrapowers as our method of obtaining non-standard models. Chapter One contains the basic logical foundations needed for the study of Non-Standard Analysis by the method of constructing ultrapowers. In Chapter Two, we look at non-standard models of topological groups and give the characterizations of some standard properties in non-standard terms. We also investigate a non-standard property that has no direct standard counterpart. In Chapter Three, we analyze an infinite field extension of a given field r and arrive at the correspondence between the subfields of our infinite field that are extensions of r and the subgroups of the corresponding Galois group through the Krull topology by non-standard methods.