As a global organisation, we, like many others, recognize the significant threat posed by the coronavirus. During this time, we have made some of our learning resources freely accessible. Our distribution centres are open and orders can be placed online. Do be advised that shipments may be delayed due to extra safety precautions implemented at our centres and delays with local shipping carriers. This volume presents the philosophical and heuristic framework Cantor developed and explores its lasting effect on modern mathematics. Cantor's ideas formed the basis for set theory and also for the mathematical treatment of the concept of infinity.
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Would you like to tell us about a lower price? If you are a seller for this product, would you like to suggest updates through seller support? 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. Read more Read less. Review ' No customer reviews. How does Amazon calculate star ratings? The machine learned model takes into account factors including: the age of a review, helpfulness votes by customers and whether the reviews are from verified purchases.
Review this product Share your thoughts with other customers. Write a customer review. Most helpful customer reviews on Amazon. Georg Cantor lived from to Judging from Hallet's bibliography, Cantor's publications on sets and infinity occurred in the years to A letter of to Richard Dedekind  is also relevant. No letter or publication by Cantor later than is discussed in Hallet's book, although a letter from to Philip Jourdain  is mentioned as outlining the proof given in the letter to Dedekind, and a partial sentence is quoted from a letter to Jourdain in Ernst Zermelo  edited Cantor's collected works in , published as Gesammelte Abhandlungen mathematischen und philosophischen Inhalts.
Hallet's book does not contain biographical details on Cantor, and it is not a general history of the rise of set theory. It is foremost an account of Cantor's conception of infinity, both metaphysical and mathematical, and of Cantor's varied presentations, in publications and letters, of his theories of cardinal and ordinal numbers.
Hallett focuses tightly on Cantor's writings as he meticulously traces the development of Cantor's ideas, and only after he has established Cantor's views does Hallett include the work of others, unless he gives a joint comparison with the focus on Cantor.
Cantor's set theory is not axiomatic, and although Hallett discusses to some degree, mainly in Part 2, the relationship of the axiomatic theory of sets to Cantor's conception of sets and infinity, the emphasis of the book is on Cantor's work, and only secondarily on the contributions of others as they explored and expanded on Cantor's ideas.
In the first two chapters of Part 2, Hallett is less concerned with how proposed axioms combine to define a theory of sets than with how certain axioms have been discussed and justified for example, as a means of limiting the comprehension of sets or of representing the iterative conception of sets and with the claim that the set theoretic paradoxes are meaningfully related to Kant's antinomies of pure reason. In the final two chapters, Hallett discusses the differing systems of Zermelo and John von Neumann , where his focus in chapter seven is on Zermelo's axiom system in relation to his and proofs of the well-ordering theorem, and in chapter eight on von Neumann's theory of ordinals from also anticipations of it by others , his use and clarification of the axiom of replacement first proposed by Abraham Fraenkel , and von Neumann's axiomatic theory of functions not sets of The Cantorian origins of set theory Introduction to Part 1: The background to the theory of the ordinals 1.
The limitation of size argument and axiomatic set theory Introduction to Part 2 5. 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.
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.
When and if they will do so, -- after all, it was last released, in its one and only paperback edition, in ! 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. Go to Amazon. Back to top. Get to Know Us. Shopbop Designer Fashion Brands. Alexa Actionable Analytics for the Web.
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Limitation of size
Would you like to tell us about a lower price? If you are a seller for this product, would you like to suggest updates through seller support? 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.
Cantorian Set Theory and Limitation of Size
Sign in Create an account. Syntax Advanced Search. About us. Editorial team. Michael Hallett.
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