Duality and Definability in First Order Logic
Author:   Michael Makkai
Publisher:   American Mathematical Society
Volume:   No. 503
ISBN:  

9780821825655


Pages:   106
Publication Date:   01 April 1994
Format:   Paperback
Availability:   Temporarily unavailable   Availability explained
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Duality and Definability in First Order Logic


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Overview

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.

Full Product Details

Author:   Michael Makkai
Publisher:   American Mathematical Society
Imprint:   American Mathematical Society
Volume:   No. 503
Weight:   0.222kg
ISBN:  

9780821825655


ISBN 10:   0821825658
Pages:   106
Publication Date:   01 April 1994
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Paperback
Publisher's Status:   Active
Availability:   Temporarily unavailable   Availability explained
The supplier advises that this item is temporarily unavailable. It will be ordered for you and placed on backorder. Once it does come back in stock, we will ship it out to you.

Table of Contents

Beth's theorem in propositional logic Factorizations in $2$-categories Definable functors Basic notions for duality The Stone-type 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.

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