Hierarchies of measure-theoretic ultrafilters

We study relations between measure-theoretic classes of ultrafilters, such as the Property M ultrafilters of {[}4], with other well-known ultrafilter classes. We define several classes of measure-theoretic ultrafilters, of which the Property M ultrafilters are the strongest. We show which containments are provable in ZFC between these measure-theoretic ultrafilters and boolean combinations of well-known ultrafilters such as the selective, semi-selective, and P-point ultrafilters. We also list some of the containment results between measure-theoretic ultrafilters and several other ultrafilter classes, such as the Arrow and Property C ultrafilters. (C) 1999 Elsevier Science B.V. All rights reserved.