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Axiomatic Set Theory by Bernays
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Since the beginning of the twentieth century, set theory, which began with Euclid's Elements and was revived in the nineteenth century, has become increasingly important in almost all areas of mathematics and logic. In Part I of this excellent monograph, A. A. Fraenkel presents an introduction to the original Zermelo-Fraenkel form of set-theoretic axiomatics and a history of its subsequent development.
In Part II Paul Bernays offers an independent presentation of a formal system of axiomatic set theory, covering such topics as the frame of logic and class theory, general set theory, transfinite recursion, completing axioms, cardinal arithmetic, and strengthening of the axiom system.
The book is directed to the reader who has some acquaintance with problems of axiomatics and with the standard methods of mathematical logic. No special knowledge of set theory and its axiomatics is presupposed. Readers will find the critical apparatus at the back of the book especially helpful. It includes indexes of authors, symbols and matters, a list of axioms, and an extensive bibliography.
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