Extensions with the approximation and cover properties have no new large cardinals

Joel David Hamkins. "Extensions with the approximation and cover properties have no new large cardinals." Fundamenta Mathematicae 180.3 (2003): 257-277. <http://eudml.org/doc/286591>.

@article{JoelDavidHamkins2003,
abstract = {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].},
author = {Joel David Hamkins},
journal = {Fundamenta Mathematicae},
keywords = {elementary embedding; large cardinals; preservation theorems; forcing},
language = {eng},
number = {3},
pages = {257-277},
title = {Extensions with the approximation and cover properties have no new large cardinals},
url = {http://eudml.org/doc/286591},
volume = {180},
year = {2003},
}

TY - JOUR
AU - Joel David Hamkins
TI - Extensions with the approximation and cover properties have no new large cardinals
JO - Fundamenta Mathematicae
PY - 2003
VL - 180
IS - 3
SP - 257
EP - 277
AB - 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].
LA - eng
KW - elementary embedding; large cardinals; preservation theorems; forcing
UR - http://eudml.org/doc/286591
ER -