Anderson (U. of Glasgow) explores collections of subsets of a finite set where the collection is described in terms of intersection, union, or inclusive conditions. He also considers more general partially ordered sets. The 1989 edition, published by University Press, Oxford, has been slightly corrected. Annotation c. Book News, Inc., Portland, OR (booknews.com) Coherent treatment provides comprehensive view of basic methods and results of the combinatorial study of finite set systems. The Clements-Lindstrom extension of the Kruskal-Katona theorem to multisets is explored, as is the Greene-Kleitman result concerning k-saturated chain partitions of general partially ordered sets. Connections with Dilworths theorem, the marriage problem, and probability are also discussed.
