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.

• 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