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Foundations of Set Theory - 2nd Edition - ISBN: 9780720422702, 9780080887050

Foundations of Set Theory, Volume 67

2nd Edition

Authors: A.A. Fraenkel Y. Bar-Hillel A. Levy
eBook ISBN: 9780080887050
Imprint: North Holland
Published Date: 1st December 1973
Page Count: 412
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Table of Contents

The Antinomies
Axiomatic Foundations of Set Theory
Type-Theoretical Approaches
Intuitionistic Conceptions of Mathematics
Metamathematical and Semantical Approaches


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.


No. of pages:
© North Holland 1973
1st December 1973
North Holland
eBook ISBN:


"...this book is a masterly survey of its field. It is lucid and concise on a technical level, it covers the historical ground admirably, and it gives a sensible account of the various philosophical positions associated with the development of the subject... essential reading for any mathematician or philosopher." --British Journal for the Philosophy of Science

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About the Authors

A.A. Fraenkel

Y. Bar-Hillel

A. Levy