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Duality and definability in first order logic
Autor: Makkai, Michael.
Rok: 1993.
ISBN: 9780821825655
OKCZID: 110341188
Citace (dle ČSN ISO 690):
MAKKAI, Michael. Duality and definability in first order logic. Providence: American Mathematical Society, 1993. x, 106 s. Memoirs of the American Mathematical Society, no. 503.
Anotace
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 well-known 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.