Let $V=L$ denote the axiom of constructibility. Are there any interesting examples of set theoretic statements which are independent of $ZFC + V=L$? And how do we construct such independence proofs? The (apparent) difficulty is as follows: Let $\phi$ be independent of $ZFC + V=L$. We want models of $ZFC + V=L + \phi$ and $ZFC + V=L + \neg\phi$. An inner model doesn't work for either one of these since the only inner model of $ZFC + V = L$ is $L$ and whatever $ZFC$ can prove to hold in $L$ is a consequence of $ZFC + V=L$. Forcing models are of no use either, since all of them satisfy $V \neq L$.