[bibtex key=Hamkins2003:ExtensionsWithApproximationAndCoverProperties]

If an extension $\bar V$ of $V$ satisfies the $\delta$-approximation and cover properties for classes and $V$ is a class in $\bar V$, then every suitably closed embedding $j:\bar V\to \bar N$ in $\bar V$ with critical point above $\delta$ restricts to an embedding $j\upharpoonright V:V\to N$ amenable to the ground model $V$. In such extensions, therefore, there are no new large cardinals above delta. This result extends work in my article on gap forcing.