Abstract
Assuming the consistency of some very large cardinals we get the consistency with ZFC of $2^{\frak{N}_n} = \mathfrak{N}_{n+1}$ for $n\lt \omega$ and $w^{\mathfrak{N}_\omega} = \mathfrak{N}_{\omega+2}$.Hence a singular cardinal can be the first cardinal which violates the Generalized Continuuum Hypothesis.
