Classifying Maximal Extensions

Abstract

In the last chapter we introduced the rudiments of a classification of the maximal extensions of Th(T^*). Work on that classification continues here. By Proposition 2.2.1 and Proposition 2.2.2, the maximal extensions of Th(T^*) correspond exactly to the ultrafilters on the index set of T when all members ofT are non-trivial. The classification presented here parallels the classification of ultrafilters. In fact, the terminology used here is intended to highlight the parallel with ultrafilters.