Abstract Set Theory PDF Download

Author: Abraham Adolf Fraenkel
Publisher:
ISBN:
Category : Set theory
Languages : en
Pages : 316

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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: A.A. Fraenkel
Publisher: Elsevier
ISBN: 0080887058
Category : Computers
Languages : en
Pages : 415

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Book Description
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.

Author: Abraham Adolf Fraenkel
Publisher:
ISBN:
Category :
Languages : en
Pages : 297

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Author: Norman T. Hamilton
Publisher: Courier Dover Publications
ISBN: 0486830470
Category : Mathematics
Languages : en
Pages : 289

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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: Daniel W. Cunningham
Publisher: Cambridge University Press
ISBN: 1107120322
Category : Mathematics
Languages : en
Pages : 265

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Book Description
Set theory can be considered a unifying theory for mathematics. This book covers the fundamentals of the subject.

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: D.C. Goldrei
Publisher: Routledge
ISBN: 1351460609
Category : Mathematics
Languages : en
Pages : 300

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Book Description
Designed for undergraduate students of set theory, Classic Set Theory presents a modern perspective of the classic work of Georg Cantor and Richard Dedekin and their immediate successors. This includes:The definition of the real numbers in terms of rational numbers and ultimately in terms of natural numbersDefining natural numbers in terms of setsThe potential paradoxes in set theoryThe Zermelo-Fraenkel axioms for set theoryThe axiom of choiceThe arithmetic of ordered setsCantor's two sorts of transfinite number - cardinals and ordinals - and the arithmetic of these.The book is designed for students studying on their own, without access to lecturers and other reading, along the lines of the internationally renowned courses produced by the Open University. There are thus a large number of exercises within the main body of the text designed to help students engage with the subject, many of which have full teaching solutions. In addition, there are a number of exercises without answers so students studying under the guidance of a tutor may be assessed.Classic Set Theory gives students sufficient grounding in a rigorous approach to the revolutionary results of set theory as well as pleasure in being able to tackle significant problems that arise from the theory.

Author: Willard Van Orman Quine
Publisher: Harvard University Press
ISBN: 9780674802070
Category : Mathematics
Languages : en
Pages : 384

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Book Description
This is an extensively revised edition of W. V. Quine’s introduction to abstract set theory and to various axiomatic systematizations of the subject. The treatment of ordinal numbers has been strengthened and much simplified, especially in the theory of transfinite recursions, by adding an axiom and reworking the proofs. Infinite cardinals are treated anew in clearer and fuller terms than before. Improvements have been made all through the book; in various instances a proof has been shortened, a theorem strengthened, a space-saving lemma inserted, an obscurity clarified, an error corrected, a historical omission supplied, or a new event noted.

Author: Thomas Scott Blyth
Publisher: Longman Publishing Group
ISBN:
Category : Mathematics
Languages : en
Pages : 238

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