[PDF] Fundamentals Of Contemporary Set Theory eBook

Author : K. J. Devlin
Publisher : Springer Science & Business Media
Page : 191 pages
File Size : 39,49 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1468400843

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This book is intended to provide an account of those parts of contemporary set theory which are of direct relevance to other areas of pure mathematics. The intended reader is either an advanced level undergraduate, or a beginning graduate student in mathematics, or else an accomplished mathematician who desires or needs a familiarity with modern set theory. The book is written in a fairly easy going style, with a minimum of formalism (a format characteristic of contemporary set theory) • In Chapter I the basic principles of set theory are developed in a "naive" tl manner. Here the notions of "set I II union " , "intersection", "power set" I "relation" I "function" etc. are defined and discussed. One assumption in writing this chapter has been that whereas the reader may have met all of these concepts before, and be familiar with their usage, he may not have considered the various notions as forming part of the continuous development of a pure subject (namely set theory) • Consequently, our development is at the same time rigorous and fast. Chapter II develops the theory of sets proper. Starting with the naive set theory of Chapter I, we begin by asking the question "What is a set?" Attempts to give a rLgorous answer lead naturally to the axioms of set theory introduced by Zermelo and Fraenkel, which is the system taken as basic in this book.

Author : Keith Devlin
Publisher : Springer Science & Business Media
Page : 204 pages
File Size : 47,88 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 146120903X

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This text covers the parts of contemporary set theory relevant to other areas of pure mathematics. After a review of "naïve" set theory, it develops the Zermelo-Fraenkel axioms of the theory before discussing the ordinal and cardinal numbers. It then delves into contemporary set theory, covering such topics as the Borel hierarchy and Lebesgue measure. A final chapter presents an alternative conception of set theory useful in computer science.

Author : Keith J. Devlin
Publisher : Springer
Page : 192 pages
File Size : 37,10 MB
Release : 1993-01-01
Category : Mengenlehre
ISBN : 9783540940944

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"This book provides an account of those parts of contemporary set theory that are relevant to other areas of pure mathematics. Intended for advanced undergraduates and beginning graduate students, the text is written in an easy-going style, with a minimum of formalism. The book begins with a review of "naive" set theory; it then develops the Zermelo-Fraenkel axioms of the theory, showing how they arise naturally from a rigorous answer to the question, "what is a set?" After discussing the ordinal and cardinal numbers, the book then delves into contemporary set theory, covering such topics as: the Borel hierarchy, stationary sets and regressive functions, and Lebesgue measure. Two chapters present an extension of the Zermelo-Fraenkel theory, discussing the axiom of constructibility and the question of provability in set theory. A final chapter presents an account of an alternative conception of set theory that has proved useful in computer science, the non-well-founded set theory of Peter Aczel"--Back cover.

Author : Joseph Breuer
Publisher : Courier Corporation
Page : 130 pages
File Size : 18,1 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 : Sean Morris
Publisher : Cambridge University Press
Page : 221 pages
File Size : 31,35 MB
Release : 2018-12-13
Category : History
ISBN : 110715250X

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Provides an accessible mathematical and philosophical account of Quine's set theory, New Foundations.

Author : Stephen Pollard
Publisher : Courier Dover Publications
Page : 196 pages
File Size : 50,63 MB
Release : 2015-07-15
Category : Mathematics
ISBN : 0486797147

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This unique approach maintains that set theory is the primary mechanism for ideological and theoretical unification in modern mathematics, and its technically informed discussion covers a variety of philosophical issues. 1990 edition.

Author : Kazimierz Kuratowski
Publisher : Elsevier
Page : 353 pages
File Size : 20,79 MB
Release : 2014-07-10
Category : Mathematics
ISBN : 1483151638

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Introduction to Set Theory and Topology describes the fundamental concepts of set theory and topology as well as its applicability to analysis, geometry, and other branches of mathematics, including algebra and probability theory. Concepts such as inverse limit, lattice, ideal, filter, commutative diagram, quotient-spaces, completely regular spaces, quasicomponents, and cartesian products of topological spaces are considered. This volume consists of 21 chapters organized into two sections and begins with an introduction to set theory, with emphasis on the propositional calculus and its application to propositions each having one of two logical values, 0 and 1. Operations on sets which are analogous to arithmetic operations are also discussed. The chapters that follow focus on the mapping concept, the power of a set, operations on cardinal numbers, order relations, and well ordering. The section on topology explores metric and topological spaces, continuous mappings, cartesian products, and other spaces such as spaces with a countable base, complete spaces, compact spaces, and connected spaces. The concept of dimension, simplexes and their properties, and cuttings of the plane are also analyzed. This book is intended for students and teachers of mathematics.

Author : Charles C Pinter
Publisher : Courier Corporation
Page : 259 pages
File Size : 33,54 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 : Herbert B. Enderton
Publisher : Academic Press
Page : 294 pages
File Size : 15,97 MB
Release : 1977-05-23
Category : Mathematics
ISBN : 0080570429

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This is an introductory undergraduate textbook in set theory. In mathematics these days, essentially everything is a set. Some knowledge of set theory is necessary part of the background everyone needs for further study of mathematics. It is also possible to study set theory for its own interest--it is a subject with intruiging results anout simple objects. This book starts with material that nobody can do without. There is no end to what can be learned of set theory, but here is a beginning.