Comment by panpog

There is only one integer k that we can actually write down (given much more paper than could fit in the universe) such that ZFC+ “BB(748)=k” is consistent. However, given that same k, ZFC+ “BB(748)≠k” is also consistent. ZFC+ “BB(748)≠k” has theorems that can be thought of as it being wrong about what “finite” means.