Memoirs of the American Mathematical Society 1993; 106 pp; softcover Volume: 105 ISBN10: 0821825658 ISBN13: 9780821825655 List Price: US$36 Individual Members: US$21.60 Institutional Members: US$28.80 Order Code: MEMO/105/503
 Using the theory of categories as a framework, this book develops a duality theory for theories in first order logic in which the dual of a theory is the category of its models with suitable additional structure. This duality theory resembles and generalizes M. H. Stone's famous duality theory for Boolean algebras. As an application, Makkai derives a result akin to the wellknown definability theorem of E. W. Beth. This new definability theorem is related to theorems of descent in category theory and algebra and can also be stated as a result in pure logic without reference to category theory. Containing novel techniques as well as applications of classical methods, this carefully written book shows attention to both organization and detail and will appeal to mathematicians and philosophers interested in category theory. Readership Mathematicians and philosophers interested in category theory and mathematical logic. Table of Contents  Beth's theorem in propositional logic
 Factorizations in \(2\)categories
 Definable functors
 Basic notions for duality
 The Stonetype adjunction for Boolean pretoposes and ultragroupoids
 The syntax of special ultramorphisms
 The semantics of special ultramorphisms
 The duality theorem
 Preparing a functor specification
 Lifting Zawadowski's argument to ultra\(^\ast\) morphisms
 The operations on \({\mathcal B}{\mathcal P}^\ast\) and UG
 Conclusion
 References
