Axiomatic Set Theory

by Patrick C. Suppes

This clear and well-developed approach to axiomatic set theory is geared toward upper-level undergraduates and graduate students. It examines the basic paradoxes and history of set theory and advanced topics such as relations and functions, equipollence, finite sets and cardinal numbers, rational and real numbers, and other subjects. 1960 edition.

Genres: Mathematics, Philosophy, Logic, Science, Nonfiction, Textbooks

Hardcover

First published January 1, 1968

Reviews

[Joseph Kulisics · Rating 5 out of 5]

I worked through all of the problems in the book. Based on my cursory assessment of other treatments of the subject, I think that the book gives one of the best treatments of axiomatic set theory that I've seen. I saw another reviewer pay special attention to the fact that the book uses a simplifying assumption, a special axiom for cardinals, to develop a cardinal arithmetic, which would ordinarily be much more complicated in its initial stages than the comparable development of ordinal arithmetic. I believe that the author later justifies the axiom with the Axiom of Choice. While a development of cardinal arithmetic independent of the Axiom of Choice and based on the rank of a set might be more intellectually parsimonious, since the Axiom of Choice is necessary to prove basic claims like the claim that the product of an infinite collection of non-empty sets is non-empty, as far as I'm concerned, the development is sufficiently rigorous and satisfying.

[Stephen · Rating 4 out of 5]

Unfortunately, many mathematics degree programs introduce set theory when convenient. This book fills in any holes that may still remain after going through your classes.

[Luca Prosperi · Rating 5 out of 5]

Spectacular reference book. All in one go...will require several detailed visits to specific chapters.

[Rick · Rating 4 out of 5]

If you want to learn Set Theory, go for a more modern treatment. If you already know Set Theory, but are interested in its history, then this is a great read.

[Mark6712]

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