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Zusatztext This is a very important book. It is essential reading for anyone working in set theory and its applications. Klappentext 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 Godel, 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. Zusammenfassung 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. Inhaltsverzeichnis 1: Basic confinalities of small reduced products 2: *N*w+1 has a Jonsson algebra 3: There are Jonsson algebras in many inaccessible cardinals 4: Jonsson algebras in inaccessibles ¿ , not ¿-Mahlo > cf(¿) > *N[0 using ranks and normal filters 6: Bounds of power of singulars: Induction 7: Strong covering lemma and CH in V[r] 8: Advanced: Cofinalities of reduced products 9: Cardinal Arithmetic Appendix 1: Colorings Appendix 2: Entangled orders and narrow Boolean algebras
