Algebras and Orders

the long version

The book consists of the lectures presented at the NATO ASI on `Algebras and Orders' held in 1991 at the Université de Montréal. The lectures cover a broad spectrum of topics in universal algebra, Boolean algebras, lattices and orders, and their links with graphs, relations, topology and theoretical computer science. More specifically, the contributions deal with the following topics: Abstract clone theory (W. Taylor); Hyperidentities and hypervarieties (D. Schweigert); Arithmetical algebras and varieties (A. Pixley); Boolean algebras with operators (B. Jonsson); Algebraic duality (B. Davey); Model-theoretic aspects of partial algebras (P. Burmeister); Free lattices (R. Freese); Algebraic ordered sets (M. Erné); Diagrams of orders (I. Rival); Essentially minimal groupoids (H. Machida, I.G. Rosenberg); and Formalization of predicate calculus (I. Fleischer). Most of the papers are up-to-date surveys written by leading researchers, or topics that are either new or have witnessed recent substantial progress. In most cases, the surveys are the first available in the literature. The book is accessible to graduate students and researchers.