3 ms·
Weird Things Happen When Math Gets Too Expressive https://www.youtube.com/watch?v=EVwQsvof7Hw https://www.youtube.com/watch?v=EVwQsvof7Hw Peano arithmetic is
by contraposit 6mo ago
Weird Things Happen When Math Gets Too Expressive
https://www.youtube.com/watch?v=EVwQsvof7Hw https://www.youtube.com/watch?v=EVwQsvof7Hw
Peano arithmetic is sufficiently expressive enough to be equivalent to any possible future theory of mathematics.
- lioeters 6mo agoEven before I started the video, I had a feeling it was going to lead to a kind of "introspective" mathematics that can reason about its own reasoning. I was not disappointed, thank you. Physics, Topology, Logic and Computation: A Rosetta Stone - https://arxiv.org/abs/0903.0340 https://arxiv.org/abs/0903.0340
- contraposit 6mo ago[dead]
- gottheUIblues 6mo agoErr? Peano Arithmetic is provably consistent in ZFC, but it is not in itself (if PA is consistent). Therefore if PA is consistent it is not equivalent to ZFC (regardless of whether ZFC is consistent or not)
- contraposit 6mo agoI am referring to this slide : https://youtu.be/EVwQsvof7Hw?t=1646 https://youtu.be/EVwQsvof7Hw?t=1646