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The main notions of set theory (cardinals, ordinals, transfinite induction) are fundamental to all mathematicians, not only to those who specialize in mathematical logic or set-theoretic topology. Basic set theory is generally given a brief overview in courses on analysis, algebra, or topology, even though it is sufficiently important, interesting, and simple to merit its own leisurely treatment. ## About book:

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This book provides just that: a leisurely exposition for a diversified audience. It is suitable for a broad range of readers, from undergraduate students to professional mathematicians who want to finally find out what transfinite induction is and why it is always replaced by Zorn's Lemma.

The text introduces all main subjects of "naive" (nonaxiomatic) set theory: functions, cardinalities, ordered and well-ordered sets, transfinite induction and its applications, ordinals, and operations on ordinals. Included are discussions and proofs of the Cantor-Bernstein Theorem, Cantor's diagonal method, Zorn's Lemma, Zermelo's Theorem, and Hamel bases. With over 150 problems, the book is a complete and accessible introduction to the subject

- Series:
**Student Mathematical Library 017** - Author:
**S. Shen, N. K. Vereshchagin** - Year:
**2002** - Publisher:
**American Mathematical Society** - Language:
**English** - ISBN:
**0-8218-2731-6,9780821827314**

- File size:
**1 704 758** - Format:
**pdf**

Security code:

A solid foundation in set theory is one of the essential preconditions of being a good, working mathematician. I have taught nearly every course in the undergraduate mathematics curriculum and the basic concepts of set theory crop up on a regular basis. I...

The main notions of set theory (cardinals, ordinals, transfinite induction) are fundamental to all mathematicians, not only to those who specialize in mathematical logic or set-theoretic topology. Basic set theory is generally given a brief overview in co...

The purpose of this book is to provide the reader who is interested in applications of fuzzy set theory, in the first place with a text to which he or she can refer for the basic theoretical ideas, concepts and techniques in this field and in the second p...

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 conc...

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 conc...

Descriptive set theory has been one of the main areas of research in set theory for almost a century. This text attempts to present a largely balanced approach, which combines many elements of the different traditions of the subject. It includes a wide va...

Presents Results from a Very Active Area of Research Exploring an active area of mathematics that studies the complexity of equivalence relations and classification problems, Invariant Descriptive Set Theory presents an introduction to the basic concep...

This is the second volume of a two-volume graduate text in set theory. The first volume covered the basics of modern set theory and was addressed primarily to beginning graduate students. This second volume is intended as a bridge between introductory set...

This volume deals with problems in the structure theory of separable infinite-dimensional Banach spaces, with a central focus on universality problems. This topic goes back to the beginnings of the field and appears in Banach's classical monograph. The no...

This is the most exhaustive study to date on natural gas hydrates. In spite of their importance, hydrates are misunderstood, and misconceptions abound. This book provides an accurate review of what hydrates are and under what conditions they will form, ...

The neurocutaneous disorders comprise a group of neurological disorders featuring skin lesions and often eye lesions, central and peripheral nervous system tumors, brain malformations, mental retardation, and psychiatric syndromes or seizures. This book p...

This classic text is widely regarded as the world's definitive and authoritative neurology reference. With state-of-the-art explanations of general neurologic principles and relevant neuroscience, the book provides experience approaches to the diagnosis a...

Looking forward to the future it is clear that today's narrow concept of fiber as a basic element for textiles, ropes and nets will become an outmoded notion. The emphasis will instead shift to new and exciting developments in fiber technology and their a...

Nitrogen in the Environment: Sources, Problems, and Management is the first volume to provide a holistic perspective and comprehensive treatment of nitrogen from field, to ecosystem, to treatment of urban and rural drinking water supplies, while also in...