Cardinal Arithmetic (Oxford Logic Guides) [Hardcover]

Saharon Shelah (Author)

Book Description

ISBN-10: 0198537859 | ISBN-13: 978-0198537854 | Publication Date: December 29, 1994

Is the continuum hypothesis still open? If we interpret it as finding the laws of cardinal arithmetic (or exponentiation, since addition and multiplication were classically solved), the hypothesis would be solved by the independence results of G�del, Cohen, and Easton, with some isolated positive results (like Gavin-Hajnal). Most mathematicians expect that only more independence results remain to be proved. In Cardinal Arithmetic, however, Saharon Shelah offers an alternative view. By redefining the hypothesis, he gets new results for the conventional cardinal arithmetic, finds new applications, extends older methods using normal filters, and proves the existence of Jonsson algebra. Researchers in set theory and related areas of mathematical logic will want to read this provocative new approach to an important topic.

Editorial Reviews

Review

"Saharon Shelah's pcf ("possible cofinalities") theory and its applications have become a major branch of set-theoretic research since the late 1980's, illuminating many issues involving singular cardinals in combinatorial set theory and the theory of large cardinals. . . .Saharon Shelah is a phenomenal mathematician, preeminent both in model theory and in set theory. His work, beginning in the early 1970's, has advanced both subjects tremendously, and even now, as he enters his fifties, he is going from strength to strength, continuing to produce results at a furious pace."--The Journal of Symbolic Logic

"The book is of considerable historical interest."--Bulletin of the American Mathematical Society

"Shelah's book on cardinal arithmetic collects his fascinating results and, in summary, is a great step forward in the development of set theory." --Mathematical Reviews

About the Author

Saharon Shelah is at The Hebrew University of Jerusalem.

Product Details

• Hardcover: 520 pages
• Publisher: Oxford University Press, USA (December 29, 1994)
• Language: English
• ISBN-10: 0198537859
• ISBN-13: 978-0198537854
• Product Dimensions: 9.3 x 6.3 x 1.3 inches
• Shipping Weight: 1.9 pounds (View shipping rates and policies)
• Amazon Best Sellers Rank: #3,145,452 in Books (See Top 100 in Books)

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