Duality and definability in first order logic / Michael Makkai.

Format:

Book

Author/Creator:

Makkai, Mihály, 1939- author.

Series:

Memoirs of the American Mathematical Society ; Volume 105, Number 503.

Memoirs of the American Mathematical Society, 0065-9266 ; Volume 105, Number 503

Language:

English

Subjects (All):

First-order logic.

Duality theory (Mathematics).

Toposes.

Physical Description:

1 online resource (122 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 1993.

Language Note:

English

Summary:

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, the author 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 carefuly written book shows an attention to both organization and detail and will appeal to mathematicians and philosophers interested in category theory.

Contents:

""Table Of Contents""; ""Abstract""; ""Introduction""; ""1. Beth's theorem for propositional logic""; ""2. Factorizations in 2-categories""; ""3. Definable functors""; ""4. Basic notions for duality""; ""5. The Stone-type adjunction for Boolean pretoposes and ultragroupoids""; ""6. The syntax of special ultramorphisms""; ""7. The semantics of special ultramorphisms""; ""8. The duality theorem""; ""9. Preparing a functor specification""; ""10. Lifting Zawadowski's argument to ultra*morphisms""; ""11. The operations in BP* and UG""; ""12. Conclusion""; ""References""

Notes:

"September 1993, Volume 105, Number 503 (fourth of 6 numbers)."

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-0080-4