Set Theory

With an Introduction to Real Point Sets

Authors: Dasgupta, Abhijit

  • Provides essential set-theoretic prerequisites for graduate work
  • Preserves a classical flavor by incorporating historical threads
  • Includes many examples of the use of set theory in topology, analysis, and algebra
  • Features flexible organization allowing a variety of topical arrangements in various courses 
  • Provides extensive problem sets for practice and challenge, many of which are designed for student participation in the development of the main material            
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  • ISBN 978-1-4614-8854-5
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Hardcover $59.99
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  • ISBN 978-1-4614-8853-8
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About this Textbook

What is a number? What is infinity? What is continuity? What is order? Answers to these fundamental questions obtained by late nineteenth-century mathematicians such as Dedekind and Cantor gave birth to set theory. This textbook presents classical set theory in an intuitive but concrete manner.

To allow flexibility of topic selection in courses, the book is organized into four relatively independent parts with distinct mathematical flavors. Part I begins with the Dedekind–Peano axioms and ends with the construction of the real numbers. The core Cantor–Dedekind theory of cardinals, orders, and ordinals appears in Part II. Part III focuses on the real continuum. Finally, foundational issues and formal axioms are introduced in Part IV. Each part ends with a postscript chapter discussing topics beyond the scope of the main text, ranging from philosophical remarks to glimpses into landmark results of modern set theory such as the resolution of Lusin's problems on projective sets using determinacy of infinite games and large cardinals.

Separating the metamathematical issues into an optional fourth part at the end makes this textbook suitable for students interested in any field of mathematics, not just for those planning to specialize in logic or foundations. There is enough material in the text for a year-long course at the upper-undergraduate level. For shorter one-semester or one-quarter courses, a variety of arrangements of topics are possible. The book will be a useful resource for both experts working in a relevant or adjacent area and beginners wanting to learn set theory via self-study.

Reviews

From the book reviews:

“This book is an excellent introduction to set theory. Dasgupta (Univ. of Detroit Mercy) promotes reader/student interaction by integrating problems throughout the text instead of just providing occasional exercise sets. … The book contains more than 630 frequently challenging exercises that will interest both upper-division students and readers with strong mathematical backgrounds. Summing Up: Highly Recommended. Upper-division undergraduates and above.” (D. P. Turner, Choice, Vol. 52 (6), February, 2015)

“This undergraduate textbook provides a thorough examination of the cardinals, ordinals, and the continuum. … This work is a good introduction and would serve for two semesters of upper undergraduate study. … Each part ends with remarks that are a departure point for further exploration. … The author’s clear interest in the subject matter and economy of presentation makes this an effective tool for learning set theory in the lecture hall or through self-study.” (Tom Schulte, MAA Reviews, November, 2014)

“The present undergraduate textbook develops the core material on cardinals, ordinals, and the real line ℝ in an informal, predominantly intuitive but nevertheless concrete and rigorous manner. … this lucidly written undergraduate set theory textbook is a welcome addition to the relevant literature, with many individual features and a remarkably high degree of thematic versatility.” (Werner Kleinert, zbMATH, Vol. 1286 (2), 2014)

Table of contents (22 chapters)

  • Preliminaries: Sets, Relations, and Functions

    Dasgupta, Abhijit

    Pages 1-23

  • The Dedekind–Peano Axioms

    Dasgupta, Abhijit

    Pages 29-46

  • Dedekind’s Theory of the Continuum

    Dasgupta, Abhijit

    Pages 47-65

  • Postscript I: What Exactly Are the Natural Numbers?

    Dasgupta, Abhijit

    Pages 67-72

  • Cardinals: Finite, Countable, and Uncountable

    Dasgupta, Abhijit

    Pages 77-107

Buy this book

eBook $44.99
price for USA (gross)
  • ISBN 978-1-4614-8854-5
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $59.99
price for USA
  • ISBN 978-1-4614-8853-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Set Theory
Book Subtitle
With an Introduction to Real Point Sets
Authors
Copyright
2014
Publisher
Birkhäuser Basel
Copyright Holder
Springer Science+Business Media New York
Distribution Rights
Distribution rights for India: Researchco Book Centre, New Delhi, India
eBook ISBN
978-1-4614-8854-5
DOI
10.1007/978-1-4614-8854-5
Hardcover ISBN
978-1-4614-8853-8
Edition Number
1
Number of Pages
XV, 444
Number of Illustrations and Tables
17 b/w illustrations
Topics