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Basic Set Theory

2012-06-11 Mathematics
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Release : 2012-06-11
Genre : Mathematics
Kind : eBook
Book Rating : 739/5 ( reviews)

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Book Synopsis Basic Set Theory by : Azriel Levy

Download or read book Basic Set Theory written by Azriel Levy. This book was released on 2012-06-11. Available in PDF, EPUB and Kindle. Book excerpt: Although this book deals with basic set theory (in general, it stops short of areas where model-theoretic methods are used) on a rather advanced level, it does it at an unhurried pace. This enables the author to pay close attention to interesting and important aspects of the topic that might otherwise be skipped over. Written for upper-level undergraduate and graduate students, the book is divided into two parts. The first covers pure set theory, including the basic notions, order and well-foundedness, cardinal numbers, the ordinals, and the axiom of choice and some of its consequences. The second part deals with applications and advanced topics, among them a review of point set topology, the real spaces, Boolean algebras, and infinite combinatorics and large cardinals. A helpful appendix deals with eliminability and conservation theorems, while numerous exercises supply additional information on the subject matter and help students test their grasp of the material. 1979 edition. 20 figures.

Basic Set Theory

2002 Mathematics
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Release : 2002
Genre : Mathematics
Kind : eBook
Book Rating : 316/5 ( reviews)

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Book Synopsis Basic Set Theory by : Nikolai Konstantinovich Vereshchagin

Download or read book Basic Set Theory written by Nikolai Konstantinovich Vereshchagin. This book was released on 2002. Available in PDF, EPUB and Kindle. Book excerpt: 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. 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.

Set Theory and its Philosophy

2004-01-15 Philosophy
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Release : 2004-01-15
Genre : Philosophy
Kind : eBook
Book Rating : 432/5 ( reviews)

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Book Synopsis Set Theory and its Philosophy by : Michael Potter

Download or read book Set Theory and its Philosophy written by Michael Potter. This book was released on 2004-01-15. Available in PDF, EPUB and Kindle. Book excerpt: Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil set theory. Potter offers a strikingly simple version of the most widely accepted response to the paradoxes, which classifies sets by means of a hierarchy of levels. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true. Set Theory and its Philosophy is a key text for philosophy, mathematical logic, and computer science.

Introduction to the Theory of Sets

2012-08-09 Mathematics
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Release : 2012-08-09
Genre : Mathematics
Kind : eBook
Book Rating : 874/5 ( reviews)

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Book Synopsis Introduction to the Theory of Sets by : Joseph Breuer

Download or read book Introduction to the Theory of Sets written by Joseph Breuer. This book was released on 2012-08-09. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Elements of Set Theory

1977-05-23 Mathematics
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Release : 1977-05-23
Genre : Mathematics
Kind : eBook
Book Rating : 429/5 ( reviews)

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Book Synopsis Elements of Set Theory by : Herbert B. Enderton

Download or read book Elements of Set Theory written by Herbert B. Enderton. This book was released on 1977-05-23. Available in PDF, EPUB and Kindle. Book excerpt: This is an introductory undergraduate textbook in set theory. In mathematics these days, essentially everything is a set. Some knowledge of set theory is necessary part of the background everyone needs for further study of mathematics. It is also possible to study set theory for its own interest--it is a subject with intruiging results anout simple objects. This book starts with material that nobody can do without. There is no end to what can be learned of set theory, but here is a beginning.

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