Thoroughly revised, updated, expanded, and reorganized to serve as a primary text for mathematics courses, Introduction to Set Theory, Third Edition covers the basics: relations, functions, orderings, finite, countable, and uncountable sets, and cardinal and ordinal numbers. It also provides five additional self-contained chapters, consolidates the material on real numbers into a single updated chapter affording flexibility in course design, supplies end-of-section problems, with hints, of varying degrees of difficulty, includes new material on normal forms and Goodstein sequences, and adds important recent ideas including filters, ultrafilters, closed unbounded and stationary sets, and partitions.
FREE Two-Day Shipping for students on millions of items. Learn more |
| ||||||||||||||||||
 Sell Back Your Copy for $23.99
Whether you buy it used on Amazon for $64.98 or somewhere else, you can sell it back through our Book Trade-In Program at the current price of $23.99.
Used Price$64.98
Trade-in Price$23.99
Price after
Trade-in$40.99 |
Book Description
Frequently Bought Together
Editorial Reviews
Review
The book remains an excellent text for a senior undergraduate or first-year graduate level course. There is sufficient material for instructors of widely differing views to assemble one-semester courses. . ..the chapter on the axiom of choice is particularly strong.
---Mathematical Reviews
. . .a fine text. . ..The proofs are both elegant and readable.
---American Mathematical Monthly
. . .offers many benefits including. . .interesting applications of abstract set theory to real analysis. . .enriching standard classroom material.
---L'Enseignement mathematique
. . .an excellent and much needed book. . .Especially valuable are a number of remarks sprinkled throughout the text which afford a glimpse of further developments.
---The Mathematical Intelligencer
The authors show that set theory is powerful enough to serve as an underlying framework for mathematics by using it to develop the beginnings of the theory of natural, rational, and real numbers.
---Quarterly Review of Applied Mathematics
. . .In the third edition, Chapter 11 has been expanded, and four new chapters have been added.
---Mathematical Reviews
---Mathematical Reviews
. . .a fine text. . ..The proofs are both elegant and readable.
---American Mathematical Monthly
. . .offers many benefits including. . .interesting applications of abstract set theory to real analysis. . .enriching standard classroom material.
---L'Enseignement mathematique
. . .an excellent and much needed book. . .Especially valuable are a number of remarks sprinkled throughout the text which afford a glimpse of further developments.
---The Mathematical Intelligencer
The authors show that set theory is powerful enough to serve as an underlying framework for mathematics by using it to develop the beginnings of the theory of natural, rational, and real numbers.
---Quarterly Review of Applied Mathematics
. . .In the third edition, Chapter 11 has been expanded, and four new chapters have been added.
---Mathematical Reviews
Product Details
Would you like to update product info or give feedback on images?
|
More About the Author
Discover books, learn about writers, read author blogs, and more.
Customer Reviews
|
Share your thoughts with other customers:
|
||||||||||||||||||||||
|
Most Helpful Customer Reviews
29 of 29 people found the following review helpful:
5.0 out of 5 stars
Close to Perfect,
By
This review is from: Introduction to Set Theory, Third Edition, Revised and Expanded (Chapman & Hall/CRC Pure and Applied Mathematics) (Hardcover)
This is pretty much the perfect introduction to set theory for someone having some familiarity with rigorous mathematics. The treatment is axiomatic but doesn't employ the usual logical formalism, everything is written in plain english. The book emphasizes the foundational character of set theory and shows how all the usual objects of mathematics can be developed using only sets. It also demonstrates the application of set theoretic methods to "ordinary" mathematics by giving complete proofs of some powerful theorems like the Hahn-Banach theorem in functional analysis. The pace is leisurely with a close look at the details. The axiom of choice is used only when necessary and it's uses are highlighted. The exercises contain real meat but are broken up in handable pieces. They also give alternative approaches to topics treated in the main text. Solutions are not contained. The last section is devoted to an outlook at more advanced set theory. The ideas of the constructible universe and of forcing are outlined, as far as that is possible on that level. There is also a discussion on candidates for additional axioms. The reader will gain both insight into what set theory is and how powerful it is. There is no better book for the same audience.
23 of 23 people found the following review helpful:
5.0 out of 5 stars
The best text I had as a graduate student,
By Charles Ashbacher (Marion, Iowa United States) - See all my reviews (TOP 500 REVIEWER) (VINE VOICE) (HALL OF FAME REVIEWER)
This review is from: Introduction to Set Theory (Pure and Applied Mathematics) (Hardcover)
One of the first classes I took as a graduate student in mathematics was in the foundations of mathematics. The topic was set theory and this was the text we used. There have been many times in my mathematical career that I have been grateful for the knowledge learned in the class and this is one of two course textbooks that I still regularly consult as a reference. It is an excellent introduction to the fundamentals of set theory and ordinal arithmetic and I heartily recommend this book to anyone teaching or learning the fundamentals of sets.
16 of 16 people found the following review helpful:
5.0 out of 5 stars
Excellent contribution!,
By Physicsmind "Physicswish" (CA United States) - See all my reviews
This review is from: Introduction to Set Theory, Third Edition, Revised and Expanded (Chapman & Hall/CRC Pure and Applied Mathematics) (Hardcover)
This is one of the best book on Set Theory in the market. The authors' exposition is highly appealing as well as clear and friendly. This is a modern Non-Naive Set Theory as against that of Halmos' famous book--Naive Set Theory. By the way, you probably don't know there is a companion book by Sigler 0387901930 Exercises in Set Theory which was an very petinent companion to both of the two famous books on Set Theory. can't miss it
Share your thoughts with other customers: Create your own review
|
|
Inside This Book
(learn more)
First Sentence:
The central concept of this book, that of a set, is, at least on the surface, extremely simple. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
Axiom of Choice, Recursion Theorem, Continuum Hypothesis, Definition Let, Induction Principle, Axiom of Constructibility, Lemma Let, Theorem Every, Zorn's Lemma, Use Exercise, Axiom of Foundation, Example Let, Ramsey's Theorem, Axiom Schema of Comprehension, Axiom of Extensionality, Axiom Schema of Replacement, Silver's Theorem, Suslin's Hypothesis, Axiom of Infinity, Axiom of Linearity, Cantor's Theorem, Axiom of Replacement, Axiom of Union, Axiom of Countable Choice, Lemma There New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
The central concept of this book, that of a set, is, at least on the surface, extremely simple. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
Axiom of Choice, Recursion Theorem, Continuum Hypothesis, Definition Let, Induction Principle, Axiom of Constructibility, Lemma Let, Theorem Every, Zorn's Lemma, Use Exercise, Axiom of Foundation, Example Let, Ramsey's Theorem, Axiom Schema of Comprehension, Axiom of Extensionality, Axiom Schema of Replacement, Silver's Theorem, Suslin's Hypothesis, Axiom of Infinity, Axiom of Linearity, Cantor's Theorem, Axiom of Replacement, Axiom of Union, Axiom of Countable Choice, Lemma There New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 36
books:
See all 36 books this book cites
100
books
cite this book:
See all 100 books citing this book
- Set Theory by Thomas Jech in Front Matter (1), Front Matter (2), and Front Matter (3)
- Fundamentals of Pattern Recognition (Chapman & Hall/CRC Pure and Applied Mathematics) by Monique L. Pavel in Front Matter (1), and Front Matter (2)
- Calculus in Vector Spaces (Chapman & Hall/CRC Pure and Applied Mathematics) by Lawrence Corwin in Front Matter (1), and Front Matter (2)
- Local Rings (Tracts in Pure & Applied Mathematics) by M. Nagata in Front Matter
- Degenerate Differential Equations in Banach Spaces (Pure and Applied Mathematics) (Chapman & Hall/CRC Pure and Applied Mathematics) by Angelo Favini in Front Matter
See all 36 books this book cites
- Qualitative Methods in Nonlinear Dynamics (Chapman & Hall/CRC Pure and Applied Mathematics) by A.A. Martynyuk in Front Matter (1), Front Matter (2), and Front Matter (3)
- C* - Algebras and Numerical Analysis (Chapman & Hall/CRC Pure and Applied Mathematics) by Ronald Hagen in Front Matter (1), Front Matter (2), and Front Matter (3)
- Qualitative Theory of Dynamical Systems (Pure and Applied Mathematics) by Anthony Michel in Front Matter (1), Front Matter (2), and Front Matter (3)
- Subplane Covered Nets (Chapman & Hall/CRC Pure and Applied Mathematics) by Norman L. Johnson in Front Matter (1), Front Matter (2), and Front Matter (3)
- Algebraic Generalizations of Discrete Groups: A Path to Combinatorial Group Theory Through One-Relator Products (Chapman & Hall/CRC Pure and Applied Mathematics) by Benjamin Fine in Front Matter (1), Front Matter (2), and Front Matter (3)
See all 100 books citing this book
What Other Items Do Customers Buy After Viewing This Item?
Tags Customers Associate with This Product(What's this?)Click on a tag to find related items, discussions, and people.
|
Sell a Digital Version of This Book in the Kindle Store
If you are a publisher or author and hold the digital rights to a book, you can sell a digital version of it in our Kindle Store.
Learn more
Customer Discussions
|
This product's forum
Active discussions in related forums
Search Customer Discussions
|
Related forums
|
Listmania!
|
|
So You'd Like to...
|
|
