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Why is it always zfc plus optionally something else? Is there anything other than zfc that creates an interesting starting point?
by daxfohl 7y ago
Why is it always zfc plus optionally something else? Is there anything other than zfc that creates an interesting starting point?
- triska 7y agoThese are excellent questions! And yes, there is! For example, I highly recommend the paper Rethinking set theory by Tom Leinster: https://arxiv.org/abs/1212.6543 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-communities/maa-awards/writing-awards/chauvenet-prizes https://www.maa.org/programs-and-communities/member-communit...
- QuesnayJr 7y agoIsn't Lawvere set theory equiconsistent with bounded Zermelo set theory? 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.
- andrepd 7y agohttps://en.m.wikipedia.org/wiki/New_Foundations https://en.m.wikipedia.org/wiki/New_Foundations
- empath75 7y agohttps://en.m.wikipedia.org/wiki/Univalent_foundations https://en.m.wikipedia.org/wiki/Univalent_foundations