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# ðŸ“™ Basic set theory by S. Shen, N. K. Vereshchagin â€” free pdf

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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**

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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...

This book consists of papers presented at the first three meetings of the Boise Extravaganza in Set Theory (BEST) at Boise State University (Idaho) in 1992, 1993, and 1994. Articles in this volume present recent results in several areas of set theory. ...

The author tried to cover everything a set theorist should master plus a representative selection of topics of current interest. That makes for a lot of ground to cover, but Jech did a great job. The writing is very well organized and clear. Every short c...

The author tried to cover everything a set theorist should master plus a representative selection of topics of current interest. That makes for a lot of ground to cover, but Jech did a great job. The writing is very well organized and clear. Every short c...

Set theory is the mathematics of infinity and part of the core curriculum for mathematics majors. This book blends theory and connections with other parts of mathematics so that readers can understand the place of set theory within the wider context. Begi...

Set theory is the mathematics of infinity and part of the core curriculum for mathematics majors. This book blends theory and connections with other parts of mathematics so that readers can understand the place of set theory within the wider context. Begi...

Set theory is the mathematics of infinity and part of the core curriculum for mathematics majors. This book blends theory and connections with other parts of mathematics so that readers can understand the place of set theory within the wider context. Begi...

Set theory is the mathematics of infinity and part of the core curriculum for mathematics majors. This book blends theory and connections with other parts of mathematics so that readers can understand the place of set theory within the wider context. Begi...