All Questions

As is well-known, the language of second-order arithmetic only has variables for natural numbers and sets of natural numbers. Higher-order objects, like functions on $\mathbb{R}$, have to be ...

Is it possible to constructively prove that every $q \in \mathbb H$ has some $r$ such that $r^2 = q$? The difficulty here is that $q$ might be a negative scalar, in which case there might be "too many"...