3
votes
2answers
663 views

Neither Even Nor Odd Natural Numbers

Modular arithmetic (MA) has the same axioms as first order Peano arithmetic (PA) except $\forall x(Sx \neq 0)$ is replaced with $\exists x(Sx=0)$. In Even XOR Odd Infinities? I asked if this statement ...
8
votes
9answers
3k views

Is PA consistent? do we know it?

1) (By Goedel's) One can not prove, in PA, a formula that can be interpreted to express the consistency of PA. (Hopefully I said it right. Specialists correct me, please). 2) There are proofs ...
6
votes
1answer
663 views

Symmetric Proof that Product is Well-Founded

This is a fairly minor, technical question, but I'll toss it out in case someone has a good idea on it. Suppose $(X,<_X)$ and $(Y,<_Y)$ are well-founded orderings (not necessarily linearly ...