[bibtex key=Hamkins2003:ExtensionsWithApproximationAndCoverProperties]

If an extension $\overline{V}$ of $V$ satisfies the $\delta$-approximation and cover properties for classes and $V$ is a class in $\overline{V}$, then every suitably closed embedding $j:\overline{V}\to \overline{N}$ in $\overline{V}$ 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.