I'm no expert, but large cardinal axioms, which are independent of the usual set theoretic ones we all know and love, are considered some of the "strongest" assumptions in math, so there might be something there. I plan to learn more about this, but it'll be months before I can say more, and that's IF I stay diligent with my studying. Stay tuned

same, but I do think the Cantor stuff is cool where you can't match different levels of infinity one to one.