User blog comment:Bubby3/Extended BEAF/@comment-223.255.230.33-20150107193238/@comment-10429372-20150110130255

First, because Loader's number is well-defined, and meameamealokkapoowa oompa is not.

Second, because Loader's function diagonalizes over all things definable in a system called higher order logic. (The actual definition is more complicated, but this is what it does).

For your other question, the answer is yes and no. meameamealokkapoowa oompa comes close to the limit of beaf, but we can of course extend, like above.