General Lattice Theory

In 20 years, tremendous progress has been made in Lattice Theory. Nevertheless, the change is in the superstructure not in the foundation. Accordingly, I decided to leave the book unchanged and add appendices to record the change. In the first appendix: Retrospective, I briefly review developments from the point of view of this book, specifically, the major results of the last 20 years and solutions of the problems proposed in this book. It is remarkable how many difficult problems have been solved! I was lucky in getting an exceptional group of people to write the other appendices: Brian A. Davey and Hilary A. Priestley on distributive lattices and duality, Friedrich Wehrung on continuous geometries, Marcus Greferath and Stefan E. Schmidt on projective lattice geometries, Peter Jipsen and Henry Rose on varieties, Ralph Freese on free lattices, Bernhard Ganter and Rudolf Wille on formal concept analysis; Thomas Schmidt collaborated with me on congruence lattices. Many of these same people are responsible for the definitive books on the same subjects. I changed very little in the book proper. The diagrams have been redrawn and the book was typeset in ~1EX. To bring the notation up-to-date, I substituted ConL for C(L), IdL for I(L), and so on. Almost 200 mathematicians helped me with this project, from correcting typos to writing long essays on the topics that should go into Retrospective. The last section of Retrospective lists the major contributors. My deeply felt thanks to all of them.

• Lattice theory
• YellowSale2006
• universal algebra

"…Grätzer’s 'General Lattice Theory' has become the lattice theorist’s bible. Now…we have the second edition, in which the old testament is augmented by a new testament…. The new testament gospel is provided by leading and acknowledged experts in their fields…. Each [of these eight contributions] is itself a gold mine. This is an excellent and engaging second edition that will long remain a standard reference."

—MATHEMATICAL REVIEWS

"Despite the large number of coauthors the style is uniform and the book is well written. As the first edition of this book had a deep influence on the development of lattice theory, I expect that the new edition will continue to hold its leading position among the books on lattice theory."

—ZENTRALBLATT MATH

"This second edition of the Gratzer's book on lattice theory is an expanded and updated form of its first edition.  Following the line of first edition, it combines the techniques of an introductory textbook with those of a monograph to introduce the reader to lattice theory and to bring the expert up to date on the most recent developments. . . Author adds eight appendices to record the changes in the superstructure of lattice theory that occurred in the time between the two editions of this book.  In the first appendix, the authro reviews the major results of the last 20 years and solutions of the problems proposed in this book. . . Almost 900 exercises form an important part of this book.  The bibliography contains over 750 entries.  A very detailed index and the Table of Notation should help the reader in finding where a concept or notation was first introduced."

---ANALELE STIINTIFICE ALE UNIVERSITATII

 

• University of Manitoba Dept. Mathematics, Winnipeg, Canada

  George Grätzer

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