Introduction to Set Theory, Revised and Expanded (Chapman & Hall/CRC Pure and Applied Mathematics) 3rd Edition by Karel Hrbacek (PDF)

Description

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.

User’s Reviews

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

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐It is a good intro book to set theory. The exercise problems range in difficulty from easy to very hard unlike Halmos’s where most of them are basically theorems which he proves eventually and are probably not meant to be solved when the student attempts it the first time. This book has a the advantage that you do not need to know logic to follow it. Most set theory books do. It would be OK for a beginner student to start with this book but after reading Enderton’s Elements of Set Theory, I feel that it is a much better book than this one.

⭐Very good text on set theory.Not for the casual reader or a beginner.The reader should be prepared to engage the materialat a mathematically serious level to profit from it.The exposition is exemplary; the material well organized.Plenty of exercises for the student.Goldrei’s text is also very good for self-study,but this book covers much more ground.

⭐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.

⭐This is aimed at undergrads, the same as Enderton’s _Elements of Set Theory_. I didn’t read the whole thing, but it seemed more clear and cohesive than that text. This is the only book I’ve found that looks like a direct alternative for Enderton. I would say, though, that it doesn’t have quite as much detail and it doesn’t have the handwavy introductions that Enderton has in some parts.

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