What do you think?
Rate this book
A Book of Set Theory
Suitable for upper-level undergraduates, this accessible approach to set theory poses rigorous but simple arguments. Each definition is accompanied by commentary that motivates and explains new concepts. Starting with a repetition of the familiar arguments of elementary set theory, the level of abstract thinking gradually rises for a progressive increase in complexity.A historical introduction presents a brief account of the growth of set theory, with special emphasis on problems that led to the development of the various systems of axiomatic set theory. Subsequent chapters explore classes and sets, functions, relations, partially ordered classes, and the axiom of choice. Other subjects include natural and cardinal numbers, finite and infinite sets, the arithmetic of ordinal numbers, transfinite recursion, and selected topics in the theory of ordinals and cardinals. This updated edition features new material by author Charles C. Pinter.
- GenresMathematicsNonfiction
259 pages, Kindle Edition
First published September 18, 2013
69 people are currently reading
187 people want to read
Ratings & Reviews
Friends & Following
Create a free account to discover what your friends think of this book!
Community Reviews
Displaying 1 - 3 of 3 reviews
January 24, 2018
This is an excellent textbook perfectly suitable for upper-level undergraduates.
Very informative, comprehensive and generally accurate, this books starts with the basic conceptual apparatus of set theory, which is then progressively developed into an array of ever more sophisticated topics, resolutely getting into post-graduate territory in the final sections of the book (when more advanced topics such as inaccessible ordinals, the relationship between the cumulative hierarchy V and the constructible universe L, elements of model theory, and issues of consistency and independence, are all treated by the author).
Well written, clear and succinct, not infested with too many typos (will I ever find an advanced mathematics book that is completely typo-free?), this is one of the best books on this utterly fascinating subject that I have found so far. The presentation of some critical concepts is also enriched with relevant historical background and interesting philosophical insights.
I also appreciated that almost all theorems are provided with a comprehensive proof (in some cases, though, some intermediate steps are not fully explained, therefore some "interpretation" or further analysis is required), and that the succession of topics is always logically coherent, and it follows a very natural progression.
The way the ordinals are treated is absolutely first-class, a brilliant examples of conceptual lucidity and intelligibility. I also particularly enjoyed the chapter where the conceptual equivalence Axiom of Choice -> Hausdorff's Maximal Principle -> Zorn's Lemma -> Well-ordering Theorem -> Axiom of Choice is explained by the author.
An excellent choice for anybody who is interested in pursuing a good level of understanding (at upper-level undergraduate depth) of this critically important subject that represents one of the conceptual foundations of modern mathematics. Yes, set theory can be a subtle, slippery realm that can quickly becomes highly technical when more sophisticated topics are studied, but this is a fundamental subject matter, representing an absolute "must-know" if really you want to comprehend the ultimate conceptual underpinning of the beautiful world of mathematics - no meaningful philosophy of mathematics can be discussed without a prior decent level of understanding of set theory.
4.5 stars, rounded up to 5 - a must-have book, a very enjoyable read, a very solid introduction to be also kept for future reference.
Very informative, comprehensive and generally accurate, this books starts with the basic conceptual apparatus of set theory, which is then progressively developed into an array of ever more sophisticated topics, resolutely getting into post-graduate territory in the final sections of the book (when more advanced topics such as inaccessible ordinals, the relationship between the cumulative hierarchy V and the constructible universe L, elements of model theory, and issues of consistency and independence, are all treated by the author).
Well written, clear and succinct, not infested with too many typos (will I ever find an advanced mathematics book that is completely typo-free?), this is one of the best books on this utterly fascinating subject that I have found so far. The presentation of some critical concepts is also enriched with relevant historical background and interesting philosophical insights.
I also appreciated that almost all theorems are provided with a comprehensive proof (in some cases, though, some intermediate steps are not fully explained, therefore some "interpretation" or further analysis is required), and that the succession of topics is always logically coherent, and it follows a very natural progression.
The way the ordinals are treated is absolutely first-class, a brilliant examples of conceptual lucidity and intelligibility. I also particularly enjoyed the chapter where the conceptual equivalence Axiom of Choice -> Hausdorff's Maximal Principle -> Zorn's Lemma -> Well-ordering Theorem -> Axiom of Choice is explained by the author.
An excellent choice for anybody who is interested in pursuing a good level of understanding (at upper-level undergraduate depth) of this critically important subject that represents one of the conceptual foundations of modern mathematics. Yes, set theory can be a subtle, slippery realm that can quickly becomes highly technical when more sophisticated topics are studied, but this is a fundamental subject matter, representing an absolute "must-know" if really you want to comprehend the ultimate conceptual underpinning of the beautiful world of mathematics - no meaningful philosophy of mathematics can be discussed without a prior decent level of understanding of set theory.
4.5 stars, rounded up to 5 - a must-have book, a very enjoyable read, a very solid introduction to be also kept for future reference.
Read
October 4, 2017Some good examples but not rigorous.
December 8, 2021
Amazing book.
Displaying 1 - 3 of 3 reviews
Can't find what you're looking for?
Get help and learn more about the design.