Is the continuum hypothesis still open? If we interpret it as finding the laws of cardinal arithmetic, it was thought to be essentially solved by the independence results of Godel and Cohen with some isolated positive results. It was expected that only more independence results remained to be proved. The author has come to change his view. 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. (shrink)