I am in the middle of watching a video of a presentation given by W. Woodin about the continuum hypothesis. This is not really something I know about, but I am confused by one of the slides (at 22:23 in the linked video). It says:
Theorem (Scott) Assume $V=L$. Then there are no measurable cardinals.
> (there are no (genuine) large cardinals)
(meta) Corollary The axiom $V=L$ is false.
Basically, I am confused as to why the non-existence of large cardinals is believed to be 'false'. From what I know large cardinals axioms are a useful thing to have, but I don't really understand why not allowing them is not just 'problematic', but 'wrong enough' to warrant that sort-of-corollary?