This is an extensively revised edition of W. V. Quine’s introduction to abstract set theory and to various axiomatic systematizations of the subject. The treatment of ordinal numbers has been strengthened and much simplified, especially in the theory of transfinite recursions, by adding an axiom and reworking the proofs. Infinite cardinals are treated anew in clearer and fuller terms than before.
Improvements have been made all through the book; in various instances a proof has been shortened, a theorem strengthened, a space-saving lemma inserted, an obscurity clarified, an error corrected, a historical omission supplied, or a new event noted.
This is the masterpiece one would have expected it to be. For the expert it is a fresh and elegant treatise, brimming deliciously with new ideas and insights. For the beginner it is a brilliant gem of exposition, rendering a host of abstruse arguments crystal clear. For all it is a smooth and exciting journey to a vivid and comprehensive view of the alternative foundations of classical mathematics.
Perhaps the most concise and readable general survey of axiomatic set theory at present available…Suitable reading not only for mathematics students…but also for philosophers with an interest in the foundations of mathematics. An excellent index and system of numbering formulae make it also a useful reference book.
This revision of an important and lucid account of the various systems of axiomatic set theory preserves the basic format and essential ingredients of its highly regarded original…There have, however, been a number of important changes, generally in the interest of greater elegance and clarity…a generally improved version of an originally masterful and brilliant work.
This book is most remarkable for its way of presenting the subject matter. A definite system of set theory is offered, but at the same time alternative ways are indicated and partly explored at every turn…The book is also remarkable for its style. Pithy, with never an unnecessary word (but with every necessary one), at times witty, the book is written in a way that is a great relief from ordinary textbooks. Quine's books always have style, but I consider this as one of the most successful from this point of view.
- 380 pages
- 5-7/8 x 9-1/4 inches
- Belknap Press
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