[Kripke]

Godel proved that the CH was consistent with the axoims of ZFC, but conjectured that it could probably be proved inconsistent as well depending on what axiom of infinity you assume. This was the proven some years after Godel's conjecture.

In other words, the CH is demonstrably unprovable on the basis of the Zermelo-Fraenkel axioms.

Maybe I phrased myself wrong. The zermelo-fraenkel axioms have of course NOT been proven inconsistent.

- Kripke