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

Volume 180 / 2003

Joel David Hamkins Fundamenta Mathematicae 180 (2003), 257-277 MSC: 03E55, 03E40. DOI: 10.4064/fm180-3-4


If an extension $V\subseteq{\overline{V}}$ 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 $j{\upharpoonright} V$ amenable to the ground model $V$. In such extensions, therefore, there are no new large cardinals above $\delta$. This result extends work in \cite{Hamkins2001:GapForcing}.


  • Joel David HamkinsThe Graduate Center of The City University of New York
    Mathematics Program
    365 Fifth Avenue New York, NY 10016, U.S.A.

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image