If an extension V ⊆ V̅ satisfies the δ approximation and cover properties for classes and V is a class in V̅, then every suitably closed embedding j: V̅ → N̅ in V̅ with critical point above δ restricts to an embedding j ↾ V amenable to the ground model V. In such extensions, therefore, there are no new large cardinals above δ. This result extends work in [Ham01].
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm180-3-4,
author = {Joel David Hamkins},
title = {Extensions with the approximation and cover properties have no new large cardinals},
journal = {Fundamenta Mathematicae},
volume = {177},
year = {2003},
pages = {257-277},
zbl = {1066.03052},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm180-3-4}
}
Joel David Hamkins. Extensions with the approximation and cover properties have no new large cardinals. Fundamenta Mathematicae, Tome 177 (2003) pp. 257-277. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm180-3-4/