[PDF] Algebraic Set Theory eBook

Author : André Joyal
Publisher : Cambridge University Press
Page : 136 pages
File Size : 38,41 MB
Release : 1995-09-14
Category : Mathematics
ISBN : 9780521558303

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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
Page : 289 pages
File Size : 29,15 MB
Release : 2018-05-16
Category : Mathematics
ISBN : 0486830470

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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
Page : 259 pages
File Size : 48,31 MB
Release : 2014-07-23
Category : Mathematics
ISBN : 0486497089

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"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
Page : 130 pages
File Size : 10,47 MB
Release : 2012-08-09
Category : Mathematics
ISBN : 0486154874

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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 : Michael Potter
Publisher : Clarendon Press
Page : 362 pages
File Size : 31,79 MB
Release : 2004-01-15
Category : Philosophy
ISBN : 0191556432

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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
Page : 516 pages
File Size : 31,13 MB
Release : 2012-05-23
Category : Mathematics
ISBN : 0486139646

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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
Page : 290 pages
File Size : 25,13 MB
Release : 2008-01-01
Category : Mathematics
ISBN : 0486462862

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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 : Jose Ferreiros
Publisher : Springer Science & Business Media
Page : 472 pages
File Size : 29,23 MB
Release : 2001-11-01
Category : Mathematics
ISBN : 9783764357498

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"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)

Author : Ilijas Farah
Publisher : Springer Nature
Page : 517 pages
File Size : 43,72 MB
Release : 2019-12-24
Category : Mathematics
ISBN : 3030270939

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This book explores and highlights the fertile interaction between logic and operator algebras, which in recent years has led to the resolution of several long-standing open problems on C*-algebras. The interplay between logic and operator algebras (C*-algebras, in particular) is relatively young and the author is at the forefront of this interaction. The deep level of scholarship contained in these pages is evident and opens doors to operator algebraists interested in learning about the set-theoretic methods relevant to their field, as well as to set-theorists interested in expanding their view to the non-commutative realm of operator algebras. Enough background is included from both subjects to make the book a convenient, self-contained source for students. A fair number of the exercises form an integral part of the text. They are chosen to widen and deepen the material from the corresponding chapters. Some other exercises serve as a warmup for the latter chapters.

Author : Joseph Landin
Publisher : Courier Corporation
Page : 275 pages
File Size : 39,1 MB
Release : 2012-08-29
Category : Mathematics
ISBN : 0486150410

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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.