Fundamentals Of Contemporary Set Theory
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Author | : K. J. Devlin |
Publisher | : Springer Science & Business Media |
Total Pages | : 191 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1468400843 |
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 |
Total Pages | : 204 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 146120903X |
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 |
Total Pages | : 192 |
Release | : 1993-01-01 |
Genre | : Mengenlehre |
ISBN | : 9783540940944 |
"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 |
Total Pages | : 130 |
Release | : 2012-08-09 |
Genre | : Mathematics |
ISBN | : 0486154874 |
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 |
Total Pages | : 221 |
Release | : 2018-12-13 |
Genre | : History |
ISBN | : 110715250X |
Provides an accessible mathematical and philosophical account of Quine's set theory, New Foundations.
Author | : Stephen Pollard |
Publisher | : Courier Dover Publications |
Total Pages | : 196 |
Release | : 2015-07-15 |
Genre | : Mathematics |
ISBN | : 0486797147 |
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 | : Judith Roitman |
Publisher | : John Wiley & Sons |
Total Pages | : 188 |
Release | : 1990-01-16 |
Genre | : Mathematics |
ISBN | : 9780471635192 |
This is modern set theory from the ground up--from partial orderings and well-ordered sets to models, infinite cobinatorics and large cardinals. The approach is unique, providing rigorous treatment of basic set-theoretic methods, while integrating advanced material such as independence results, throughout. The presentation incorporates much interesting historical material and no background in mathematical logic is assumed. Treatment is self-contained, featuring theorem proofs supported by diagrams, examples and exercises. Includes applications of set theory to other branches of mathematics.
Author | : Charles C Pinter |
Publisher | : Courier Corporation |
Total Pages | : 259 |
Release | : 2014-07-23 |
Genre | : Mathematics |
ISBN | : 0486497089 |
"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 | : |
Publisher | : Univalent Foundations |
Total Pages | : 484 |
Release | : |
Genre | : |
ISBN | : |
Author | : A.A. Fraenkel |
Publisher | : Elsevier |
Total Pages | : 415 |
Release | : 1973-12-01 |
Genre | : Computers |
ISBN | : 0080887058 |
Foundations of Set Theory discusses the reconstruction undergone by set theory in the hands of Brouwer, Russell, and Zermelo. Only in the axiomatic foundations, however, have there been such extensive, almost revolutionary, developments. This book tries to avoid a detailed discussion of those topics which would have required heavy technical machinery, while describing the major results obtained in their treatment if these results could be stated in relatively non-technical terms. This book comprises five chapters and begins with a discussion of the antinomies that led to the reconstruction of set theory as it was known before. It then moves to the axiomatic foundations of set theory, including a discussion of the basic notions of equality and extensionality and axioms of comprehension and infinity. The next chapters discuss type-theoretical approaches, including the ideal calculus, the theory of types, and Quine's mathematical logic and new foundations; intuitionistic conceptions of mathematics and its constructive character; and metamathematical and semantical approaches, such as the Hilbert program. This book will be of interest to mathematicians, logicians, and statisticians.