...typo on a particular post that I edited and re-posted, but not overall, assuming there are any.

Ok. Baby girl turned a week old today and then I came down with a case of the sniffles so I got banned from being near baby and instead have been doing all the laundry, dishes, etc.

I really do understand what was wrong with my original post. I thought, hey, we can't have a regular sequence that will be unbounded in $\omega_1$, but maybe we don't need one. At least, we can assume there isn't one and derive a contradiction. That works too, and that is exactly what I did. I assumed all the standard stuff and derived a contradiction... Set theory has been waiting for that one axiom that would tidy things up. Right now it's just a game of assume this and prove that but assume this and instead prove that. We haven't found the answer. I think we assume the axiom of choice, then assert both statements #1 and #2 (one of which must be true) imply that $\omega_1$ cannot exist, and we put to bed the long standing issue of the continuum. I'm all ears if you find something wrong and as always, I'm happy to be the crank until then.