It’s not about what you can prove, it’s what you can state. The first-order theory of the reals doesn’t even have the concepts to state such a thing. If your base theory is the reals, then sets of reals are a second-order notion.
It’s not about what you can prove, it’s what you can state. The first-order theory of the reals doesn’t even have the concepts to state such a thing. If your base theory is the reals, then sets of reals are a second-order notion.