A monograph containing a historical introduction by A. A. Fraenkel to the original Zermelo-Fraenkel form of set-theoretic axiomatics, and Paul Bernays’ independent presentation of a formal system of axiomatic set theory. No special knowledge of set thory and its axiomatics is required. With indexes of authors, symbols and matters, a list of axioms and an extensive bibliography.
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8 of 8 people found the following review helpful:
4.0 out of 5 stars
A Work of Art,
By
This review is from: Axiomatic Set Theory (Dover Books on Mathematics) (Paperback)
This book is not suitable as an introduction to set theory. The writing is extremely awkward. I'm not sure, but it seems as though Bernays wrote it himself, and English was not his first language. More importantly, Bernays is not focused on presenting the concepts of set theory in a way that is intuitively easy to grasp. Rather, he is presenting a formal axiomatic theory of sets that presents the concepts of set theory in a mathematically elegant way.
The reason I gave this book four stars, despite the lack of readability, is that the formal system presented by Bernays is, in my opinion, a mathematical work of art. One cannot hope for a better system. It does all the things a formal system is supposed do, and with elegance. The logical relations between the intuitive concepts and propositions of set theory are made explicit. No aspect of the system has been ignored or given a sloppy, makeshift solution (as is the case, for example, with Quine's "Mathematical Logic" and especially Russell and Whitehead's "Principia"). Because of this, it is an excellent tool for sharpening one's conception of set theoretic concepts and gives an aesthetically pleasing presentation of them. Briefly, if you are looking for a good introduction to set theory, this is not it, but for the set theory/formal system enthusiast it is a masterpiece.
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