Algebraic Set Theory PDF Download
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Author: André Joyal
Publisher: Cambridge University Press
ISBN: 9780521558303
Category : Mathematics
Languages : en
Pages : 136
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Book Description
This book offers a new algebraic approach to set theory. The authors introduce a particular kind of algebra, the Zermelo-Fraenkel algebras, which arise from the familiar axioms of Zermelo-Fraenkel set theory. Furthermore, the authors explicitly construct these algebras using the theory of bisimulations. Their approach is completely constructive, and contains both intuitionistic set theory and topos theory. In particular it provides a uniform description of various constructions of the cumulative hierarchy of sets in forcing models, sheaf models and realizability models. Graduate students and researchers in mathematical logic, category theory and computer science should find this book of great interest, and it should be accessible to anyone with a background in categorical logic.
Author: André Joyal
Publisher: Cambridge University Press
ISBN: 9780521558303
Category : Mathematics
Languages : en
Pages : 136
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Book Description
This book offers a new algebraic approach to set theory. The authors introduce a particular kind of algebra, the Zermelo-Fraenkel algebras, which arise from the familiar axioms of Zermelo-Fraenkel set theory. Furthermore, the authors explicitly construct these algebras using the theory of bisimulations. Their approach is completely constructive, and contains both intuitionistic set theory and topos theory. In particular it provides a uniform description of various constructions of the cumulative hierarchy of sets in forcing models, sheaf models and realizability models. Graduate students and researchers in mathematical logic, category theory and computer science should find this book of great interest, and it should be accessible to anyone with a background in categorical logic.
Author: Norman T. Hamilton
Publisher: Courier Dover Publications
ISBN: 0486830470
Category : Mathematics
Languages : en
Pages : 289
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Book Description
This text is formulated on the fundamental idea that much of mathematics, including the classical number systems, can best be based on set theory. 1961 edition.
Author: Charles C Pinter
Publisher: Courier Corporation
ISBN: 0486497089
Category : Mathematics
Languages : en
Pages : 259
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Book Description
"This accessible approach to set theory for upper-level undergraduates poses rigorous but simple arguments. Each definition is accompanied by commentary that motivates and explains new concepts. A historical introduction is followed by discussions of classes and sets, functions, natural and cardinal numbers, the arithmetic of ordinal numbers, and related topics. 1971 edition with new material by the author"--
Author: Joseph Breuer
Publisher: Courier Corporation
ISBN: 0486154874
Category : Mathematics
Languages : en
Pages : 130
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Book Description
This undergraduate text develops its subject through observations of the physical world, covering finite sets, cardinal numbers, infinite cardinals, and ordinals. Includes exercises with answers. 1958 edition.
Author: Krzysztof Ciesielski
Publisher: Cambridge University Press
ISBN: 9780521594653
Category : Mathematics
Languages : en
Pages : 256
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Book Description
Presents those methods of modern set theory most applicable to other areas of pure mathematics.
Author: Michael Potter
Publisher: Clarendon Press
ISBN: 0191556432
Category : Philosophy
Languages : en
Pages : 362
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Book Description
Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil set theory. Potter offers a strikingly simple version of the most widely accepted response to the paradoxes, which classifies sets by means of a hierarchy of levels. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true. Set Theory and its Philosophy is a key text for philosophy, mathematical logic, and computer science.
Author: Robert R. Stoll
Publisher: Courier Corporation
ISBN: 0486139646
Category : Mathematics
Languages : en
Pages : 516
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Book Description
Explores sets and relations, the natural number sequence and its generalization, extension of natural numbers to real numbers, logic, informal axiomatic mathematics, Boolean algebras, informal axiomatic set theory, several algebraic theories, and 1st-order theories.
Author: John L. Bell
Publisher: Courier Corporation
ISBN: 0486462862
Category : Mathematics
Languages : en
Pages : 290
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Book Description
This text introduces topos theory, a development in category theory that unites important but seemingly diverse notions from algebraic geometry, set theory, and intuitionistic logic. Topics include local set theories, fundamental properties of toposes, sheaves, local-valued sets, and natural and real numbers in local set theories. 1988 edition.
Author: Joseph Landin
Publisher: Courier Corporation
ISBN: 0486150410
Category : Mathematics
Languages : en
Pages : 275
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Book Description
This self-contained text covers sets and numbers, elements of set theory, real numbers, the theory of groups, group isomorphism and homomorphism, theory of rings, and polynomial rings. 1969 edition.
Author: Jose Ferreiros
Publisher: Springer Science & Business Media
ISBN: 9783764357498
Category : Mathematics
Languages : en
Pages : 472
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Book Description
"José Ferreirós has written a magisterial account of the history of set theory which is panoramic, balanced, and engaging. Not only does this book synthesize much previous work and provide fresh insights and points of view, but it also features a major innovation, a full-fledged treatment of the emergence of the set-theoretic approach in mathematics from the early nineteenth century. This takes up Part One of the book. Part Two analyzes the crucial developments in the last quarter of the nineteenth century, above all the work of Cantor, but also Dedekind and the interaction between the two. Lastly, Part Three details the development of set theory up to 1950, taking account of foundational questions and the emergence of the modern axiomatization." (Bulletin of Symbolic Logic)
