Is the continuum hypothesis still open?
If we interpret it as finding the laws of cardinal arithmetic (really exponentiation since addition and multiplication were classically solved), it was thought to be essentially solved by the independence results of Gödel and Cohen (and Easton) with some isolated positive results (like Galvin-Hajnal). It was expected that only more independence results remained to be proved.
The author has come to change his view: we should stress Π]*N0 (not 2]Π) and mainly look at the cofinalities rather than cardinalities, in particular pp (µ), pcf (α). Their properties are investigated here and conventional cardinal arithmetic is reduced to 2]*N (*N - regular, cases totally independent) and various cofinalities. 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.
- ISBN10 0198537859
- ISBN13 9780198537854
- Publish Date 17 November 1994
- Publish Status Active
- Publish Country GB
- Publisher Oxford University Press
- Imprint Clarendon Press
- Format Hardcover
- Pages 512
- Language English