| Introduction to Cardinal Arithmetic 1999 Edition Contributor(s): Holz, Michael (Author), Steffens, Karsten (Author), Weitz, E. (Author) |
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ISBN: 3764361247 ISBN-13: 9783764361242 Publisher: Birkhauser OUR PRICE: $94.05 Product Type: Hardcover - Other Formats Published: September 1999 Annotation: This book is an introduction into modern cardinal arithmetic in the frame of the axioms of Zermelo-Fraenkel set theory together with the axiom of choice. A first part describes the classical theory developed by Bernstein, Cantor, Hausdorff, Kvnig and Tarski between 1870 and 1930. Next, the development in the seventies led by Galvin, Hajnal and Silver is characterized. The third part presents the fundamental investigations in pcf theory which have been worked out by Shelah to answer the questions left open in the seventies. This text is the first self-contained introduction to cardinal arithmetic which also includes pcf theory. It is aimed at undergraduates, and also at postgraduate students and researchers who want to broaden their knowledge of cardinal arithmetic. It gives a relatively complete survey of results provable in ZFC. |
| Additional Information |
| BISAC Categories: - Mathematics | Set Theory - Mathematics | Discrete Mathematics - Mathematics | Logic |
| Dewey: 511.322 |
| LCCN: 99038071 |
| Series: Birkhduser Advanced Texts / Basler Lehrb]cher |
| Physical Information: 0.85" H x 6.77" W x 9.45" (1.50 lbs) 304 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: This book is an introduction to modern cardinal arithmetic, developed in the frame of the axioms of Zermelo-Fraenkel set theory together with the axiom of choice. It splits into three parts. Part one, which is contained in Chapter 1, describes the classical cardinal arithmetic due to Bernstein, Cantor, Hausdorff, Konig, and Tarski. The results were found in the years between 1870 and 1930. Part two, which is Chapter 2, characterizes the development of cardinal arith- metic in the seventies, which was led by Galvin, Hajnal, and Silver. The third part, contained in Chapters 3 to 9, presents the fundamental investigations in pcf-theory which has been developed by S. Shelah to answer the questions left open in the seventies. All theorems presented in Chapter 3 and Chapters 5 to 9 are due to Shelah, unless otherwise stated. We are greatly indebted to all those set theorists whose work we have tried to expound. Concerning the literature we owe very much to S. Shelah's book Sh5] and to the article by M. R. Burke and M. Magidor BM] which also initiated our students' interest for Shelah's pcf-theory. |