> But inside the model there really isn't a bijection between the sets of naturals and reals No. Inside the model, there is exactly such a surjection. We don't

> But inside the model there really isn't a bijection between the sets of naturals and reals No. Inside the model, there is exactly such a surjection. We don't care what happens outside of it. Maybe you already knew this, but to clarify: "Countable" means that there exists a surjection, not necessarily a bijection. For instance, the set {a,b,c} is countable, but there is clearly no bijection Nat -> {a,b,c} as one set is infinite and the other's finite. > It's not too surprising On the contrary: It's a ground-breaking result IMO.