Cantorian Set Theory and Limitation of Size (Oxford Logic Guides) (Hardcover)

by Michael Hallett (Author) "Cantor was the founder of the mathematical theory of the infinite, and so one might with justice call him the founder of modern mathematics..." (more)
Key Phrases: aleph theorem, modern axiomatic set theory, set existence principles, Cantor Nachlass, Zermelo Nachlass, Summa Theologica (more...)

Editorial Reviews

Review

"Here is the first full-length study to do justice both to the mathematical importance of Cantor's work and to the philosophical ideas that governed it....The book is very well informed mathematically, yet much of Hallett's perceptive comment on and his patient and sympathetic interpretation of the philosophical ideas of Cantor and the other founders of set theory will be readily intelligible to nonspecialists, making the book of great interest to mathematician and philosopher alike."--Choice
"Establishes a new plateau for historical comprehension of Cantor's monumental contribution to mathematics."--The American Mathematical Monthly
--This text refers to the Paperback edition.

Product Description
Cantor's ideas formed the basis for set theory and also for the mathematical treatment of the concept of infinity. The philosophical and heuristic framework he developed had a lasting effect on modern mathematics, and is the recurrent theme of this volume. Hallett explores Cantor's ideas and, in particular, their ramifications for Zermelo-Frankel set theory. --This text refers to the Paperback edition.

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Product Details

• Hardcover: 364 pages
• Publisher: Oxford University Press, USA (November 1, 1984)
• Language: English
• ISBN-10: 0198531796
• ISBN-13: 978-0198531791
• Product Dimensions: 9.5 x 6.2 x 0.9 inches
• Shipping Weight: 1.6 pounds
• Average Customer Review: 5.0 out of 5 stars See all reviews (1 customer review)
• Amazon.com Sales Rank: #4,566,347 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

2 of 2 people found the following review helpful:

5.0 out of 5 stars By far the BEST book on the development of Cantor's ideas., August 4, 2008

By	William D. Fusfield - See all my reviews (REAL NAME)

This review is from: Cantorian Set Theory and Limitation of Size (Oxford Logic Guides) (Paperback)

This is BY FAR the best and most INTERESTING book available on how Cantor developed his key ideas about transfinite sets, large cardinals, ordinals etc. It contains materials that will be highly relevant to even the most advanced set theorists, while yet managing to be generally accessible to those who, like myself, have only around a B.S. mathematics degree level of understanding of the field. This ability to be of use and interest to readers with such widely varied mathematical preparations is a true tribute to the author's gift for being able to explain even very advanced concepts clearly and directly, something which is evident throughout the text, -- and unfortunately sorely missing in most mathematical texts operating at such a high level of abstraction. To be a bit more precise, I hope, persons with only a basic understanding of set theory -- something around what one should be able to glean from reading, say, Halmos' "Naive Set Theory" -- will indeed find themselves "out at sea" at times, but actually surprisingly FEW times, considering how well the author manages to unpack most of the key concepts and draw you back into the primary narrative. No doubt because this book is so much better than all its competitors, used copies, even the paperbacks, are now selling for a small fortune. [I kid you not, I just saw one listed at over $990!; though a few minutes of searching the main web book seller consolidators -- including the listings here at Amazon -- should still bag you one for under $100, at least if you act reasonably soon.] Clearly the publisher really needs to reissue this work to meet the fully justified demand! When and if they will do so, -- after all, it was last released, in its one and only paperback edition, in 1986! -- is anybody's guess. So, if you are a Cantor scholar, or a serious set theorist of any persuasion, you should probably bite the bullet and buy one now before the price really goes through the roof and you have to rely on marked-up, slowly disappearing library copies, -- until, that is, they all get stolen and resold on the web, which has happened to several classic math works already. One last thing, for those who don't really need the most sophisticated work on Cantor's intellectual development, Joseph Dauben's biography of Cantor is also very good and still widely available at a reasonable price. [His biography of Abraham Robinson is also very good by the way.]