Interesting extra refs on large cardinals mentioned by the video:
1. Large cardinals: https://en.wikipedia.org/wiki/List_of_large_cardinal_propert...
2. Berkeley cardinal (larger than any described on the video): https://en.wikipedia.org/wiki/Berkeley_cardinal
3. Presentation for those looking for a TL;DR: https://math.berkeley.edu/~jhicks/links/SOTS/cskipper112613....
4: The upper attic, (how far can we take this?): http://cantorsattic.info/Upper_attic
5: Kunen inconsistency (it seems we can take it pretty far): http://cantorsattic.info/Kunen_inconsistency