Good ultrafilters and highly saturated models: a friendly explanation

Abstract

Highly saturated models are a fundamental part of the model-theoretic machinery of nonstandard analysis. Of the two methods for producing them, ultrapowers constructed with the aid of $\kappa^+$-good ultrafilters seems by far the less popular. Motivated by the hypothesis that this is partly due to the standard exposition being somewhat dense, a presentation is given which is designed to be easier to digest.