4 ms·
Are you more comfortable with a different set of foundations? Intuitionistic? Finitistic or non-completable infinities?
by bordercases 8y ago
Are you more comfortable with a different set of foundations? Intuitionistic? Finitistic or non-completable infinities?
- antidesitter 8y agoCan a statement like Goodstein's theorem (which is about finite objects) be proven by finitist mathematics? It cannot be proven by Peano arithmetic, which is bi-interpretable with ZFC with the axiom of infinity replaced by its negation [1], or any weaker theory. [1] https://math.stackexchange.com/questions/315399/how-does-zfc-infinitythere-is-no-infinite-set-compare-with-pa https://math.stackexchange.com/questions/315399/how-does-zfc...