Topological Duality for Distributive Lattices
Theory and Applications

Introduces lattice-theoretic and topological methods in logic and computer science, with applications in domain theory and automata theory.

Mai Gehrke (Author), Sam van Gool (Author)

9781009349697, Cambridge University Press

Hardback, published 7 March 2024

367 pages
25.1 x 17.5 x 2.5 cm, 0.8 kg

'Duality is an indispensable tool in logic and theoretical computer science, and this book provides a great introduction to it. It is very pleasant to read, and does a wonderful job explaining the key ideas. It is highly recommended to anyone entering the field.' Yde Venema, Universiteit van Amsterdam

Introducing Stone–Priestley 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.

Subject Areas: Mathematical theory of computation [UYA]