Cardinal Arithmetic

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 Gödel, 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 redefin…