For example, I highly recommend the paper Rethinking set theory by Tom Leinster:
https://arxiv.org/abs/1212.6543
It highlights Lawvere set theory. The paper won this year's Chauvenet Prize:
https://www.maa.org/programs-and-communities/member-communit...
ZFC, its subtheories, and its extensions, serve as a universal yardstick for consistency results. It's not really clear why that is the case, but it has so far proven to be so.
ZFC, its subtheories, and its extensions, serve as a universal yardstick for consistency results. It's not really clear why that is the case, but it has so far proven to be so.