Cardinal Arithmetic
Cardinal Arithmetic
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Summary
Setting a new direction in research in the subject, this book presents a new view of cardinal arithmetic, one of the central issues in set theory. Focusing on cofinalities rather than cardinalities, new results are obtained and published here for the first time.
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Cardinal Arithmetic by Saharon Shelah
Is the continuum hypothesis still open? If we interpret it as finding the laws of cardinal arithmetic (really exponentiation since addition and multiplication were classically solved), it was thought to be essentially solved by the independence results of Gödel and Cohen (and Easton) with some isolated positive results (like Galvin-Hajnal). It was expected that only more independence results remained to be proved. The author has come to change his view: we should stress Π]*N0 (not 2]Π) and mainly look at the cofinalities rather than cardinalities, in particular pp (μ), pcf (α). Their properties are investigated here and conventional cardinal arithmetic is reduced to 2]*N (*N - regular, cases totally independent) and various cofinalities. This enables us to get new results for the conventional cardinal arithmetic, thus supporting the interest in our view. We also find other applications, extend older methods of using normal fiters and prove the existence of Jonsson algebra.
The mathematics here will remain an important summit of the subject and the Editors have the good fortune of having obtained a landmark volume for the Logic Guide Series* Proceedings of the Edinburgh Mathematical Society 1998 (41) *
This book is a great step forward in the development of set theory. * Mathematical Reviews Clipping. *
This is a very important book. It is essential reading for anyone working in set theory and its applications. * Bull.London Math.Soc. *
This book is a great step forward in the development of set theory. * Mathematical Reviews Clipping. *
This is a very important book. It is essential reading for anyone working in set theory and its applications. * Bull.London Math.Soc. *
Shelah, Saharon: - Saharon Shelah works in the Institute of Mathematics at the Hebrew University of Jerusalem and in the Department of Mathematics at Rutgers University, New Jersey.
| SKU | Unavailable |
| ISBN 13 | 9780198537854 |
| ISBN 10 | 0198537859 |
| Title | Cardinal Arithmetic |
| Author | Saharon Shelah |
| Series | Oxford Logic Guides |
| Condition | Unavailable |
| Publisher | Oxford University Press |
| Year published | 1994-11-17 |
| Number of pages | 512 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |