[FOM] Cohen's Minimal Model and others

[Monroe Eskew]

On Fri, May 8, 2009 at 9:07 PM, <joeshipman at aol.com> wrote:
> What other results of this kind are there? Hamkins has shown that a
> certain very large cardinal axiom (larger than n-huge for all n), if
> consistent, is consistent with V=HOD, but I am looking for results in
> the other direction, that show an inconsistency of a large cardinal
> axiom with "V=X" for various inductively defined classes X.

Here's one: If there is a strongly compact cardinal, then V is not
L[A] for any A.  See Jech, p. 366.