Bücher von W. W. Comfort

An ultrafilter is a truth-value assignment to the family of subsets of a set, and a method of convergence to infinity. The model-theoretic property finds its expression in the construction of the ultraproduct and the compactness type of theorem of Los (implying the compactness theorem of first-order logic);

A chain condition is a property, typically involving considerations of cardinality, of the family of open subsets of a topological space.