TITLE: Failure of the GCH
QUESTION [9 upvotes]: What is the (currently known) consistency strength of global failure of the GCH?
I do not have access to the exact statement of the original Foreman-Woodin result. My searches seem to indicate that they used an assumption at the region of a supercompact, although I have seen comments stating that the result has been improved to require something in the region of a hypermeasurable. Is this correct? What this exact upper bound?
Thanks a lot.

REPLY [9 votes]: By work of Gitik-Mitchell a $(\kappa+2)$-strong cardinal $\kappa$ is required, and by work of Merimovich a  $(\kappa+3)$-strong cardinal $\kappa$ (in fact a cardinal $\kappa$ with $o(\kappa)=\kappa^{++}+\kappa^{+}$) is enough. Gitik and Merimovich have a project to get the total failure of $GCH$ from optimal hypotheses. It's yet incomplete. If I remember it correctly, it says something like this:
Theorem. The following are equiconsistent:
1-For any $\alpha$, there are stationary many cardinals $\kappa$ with $o(\kappa)=\kappa^{++}+\alpha,$
2-GCH fails everywhere,
3-$\forall \lambda, 2^{\lambda}=\lambda^{++}.$