General Lattice Theory: Volume 1: The Foundation Book

From the first edition: "This book combines the techniques of an introductory text with those of a monograph to introduce the general reader to lattice theory and to bring the expert up to date on the most recent developments. The first chapter, along with a selection of topics from later chapters, can serve as an introductory course covering first concepts, distributive, modular, semimodular, and geometric lattices, and so on. About 900 exercises and almost 130 diagrams help the beginner to learn the basic results and important techniques. The latter parts of each chapter give deeper developments of the fields mentioned above and there are chapters on equational classes (varieties) and free products. More advanced readers will find the almost 200 research problems, the extensive bibliography, and the further topics and references at the end of each chapter of special use." In this present edition, the work has been significantly updated and expanded. It contains an extensive new bibliography of 530 items and has been supplemented by eight appendices authored by an exceptional group of experts. The first appendix, written by the author, briefly reviews developments in lattice theory, specifically, the major results of the last 20 years and solutions of the problems proposed in the first edition. The other subjects concern distributive lattices and duality (Brian A. Davey and Hilary A. Priestley), continuous geometries (Friedrich Wehrung), projective lattice geometries (Marcus Greferath and Stefan E. Schmidt), varieties (Peter Jipsen and Henry Rose), free lattices (Ralph Freese), formal concept analysis (Bernhard Ganter and Rudolf Wille), and congruence lattices (Thomas Schmidt in collaboration with the author). This is an unchanged reprint, in softcover, of the second (hardcover) edition of this classic book on lattice theory by one of the leading figures of the field. Appendices cover the recent developments.Read More