Topological Duality for Distributive Lattices: Theory and Applications [Hardcover]

Introduces lattice-theoretic and topological methods in logic and computer science, with applications in domain theory and automata theory.This introduction to StonePriestley duality theory brings modern tools in the area together in textbook format for the first time and covers applications to logic and theoretical computer science. This book is for undergraduates, graduate students, and researchers in lattice theory, algebra, topology, logic, and theoretical computer science.This introduction to StonePriestley duality theory brings modern tools in the area together in textbook format for the first time and covers applications to logic and theoretical computer science. This book is for undergraduates, graduate students, and researchers in lattice theory, algebra, topology, logic, and theoretical computer science.Introducing StonePriestley duality theory and its applications to logic and theoretical computer science, this book equips graduate students and researchers with the theoretical background necessary for reading and understanding current research in the area. After giving a thorough introduction to the algebraic, topological, logical, and categorical aspects of the theory, the book covers two advanced applications in computer science, namely in domain theory and automata theory. These topics are at the forefront of active research seeking to unify semantic methods with more algorithmic topics in finite model theory. Frequent exercises punctuate the text, with hints and references provided.Preface; 1. Order and lattices; 2. Topology and order; 3. Priestley duality; 4. Duality methods; 5. Categorical duality; 6. Omega-point duality; 7. Domain theory; 8. Automata theory; Bibliography; Notation; Index.This book introduces efficiently Stone-Priestley duality theory for bounded distributive lattices, thereby laying solid mathematical foundations for applications in mathematics and computer science. Readers interested in the fields of domain theory and automatalS0