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This simple introductory treatment emphasizes fundamentals and is easily comprehensible to readers with some college algebra. Topics include rudiments; arbitrary sets and their cardinal numbers; ordered sets and their ordered types; and well-ordered…

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Confusing Textbooks? Missed Lectures? Not Enough Time? Fortunately for you, there's Schaum's Outlines. More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher…

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The concept of infinity has been for hundreds of years one of the most fascinating and elusive ideas to tantalize the minds of scholars and lay people alike. The theory of infinite sets lies at the heart of much of mathematics, yet is has produced a series of…

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In this introduction to set theory and logic, the author discusses first order logic, and gives a rigorous axiomatic presentation of Zermelo-Fraenkel set theory. He includes many methodological remarks and explanations, and demonstrates how the basic concepts of…

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The authors present some surprising connections that sets of uniqueness for trigonometic series have with descriptive set theory. They present many new results concerning the structure of sets of uniqueness and include solutions to some of the classical problems…

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The intention of this book is to give the necessary and sufficient conditions for a C map to be C stable, this objective being achieved in a wide range of dimensions via a detailed study of the geometry and topology of many classes of generic singularities. The…

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A succinct introduction to mathematical logic and set theory, which together form the foundations for the rigorous development of mathematics. Suitable for all introductory mathematics undergraduates, Notes on Logic and Set Theory covers the basic concepts of…

Naive Set Theory

by P. R. Halmos

|October 24, 1974

Hardcover

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From the Reviews: "...He (the author) uses the language and notation of ordinary informal mathematics to state the basic set-theoretic facts which a beginning student of advanced mathematics needs to know. ...Because of the informal method of presentation, the…

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This text presents methods of modern set theory as tools that can be usefully applied to other areas of mathematics. The author describes numerous applications in abstract geometry and real analysis and, in some cases, in topology and algebra. The book begins…

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The theory of sets of multiples, a subject that lies at the intersection of analytic and probabilistic number theory, has seen much development since the publication of "Sequences" by Halberstam and Roth nearly thirty years ago. The area is rich in problems, many…

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During the past 25 years, set theory has developed in several interesting directions. The most outstanding results cover the application of sophisticated techniques to problems in analysis, topology, infinitary combinatorics and other areas of mathematics. This…

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Set theory is concerned with the foundation of mathematics. In the original formulations of set theory, there were paradoxes contained in the idea of the "set of all sets". Current standard theory (Zermelo-Fraenkel) avoids these paradoxes by restricting the way…