Power set at ${\aleph }_{\omega }$: On a theorem of Woodin

Abstract

We give Woodin's original proof that if there exists a $(\kappa +2)-$strong cardinal $\kappa ,$ then there is a generic extension of the universe in which $\kappa ={\aleph }_{\omega },$ $GCH$ holds below ${\aleph }_{\omega }$ and $2^{{\aleph }_{\omega }}={\aleph }_{\omega +2}.$