[FOM] Height and Width of the universe

[Ilya Tsindlekht]

On Sun, Jan 20, 2008 at 12:09:08PM -0500, joeshipman at aol.com wrote:
> Here are two theorems of the form "If the Universe is tall enough, it 
> can't be too narrow."
> 
> If there is a measurable cardinal, there is a nonconstructible set.
> If there is an inaccessible cardinal, there is a countable transitive 
> model of ZFC.
[...]
Does this relate Universe height to its width? What this theorem really
says is that aleph_1-complete ulnrafilter cannot be constructive.