In classical recursion theory, given a set $x \le_T 0'$, one can construct a set $y \le_T 0'$ such that $x$ and $y$ are incomparable.
Is the following analogous statement in hyperarithmetical theory true: given a set (of naturals) $x \in \Delta^1_2$, one can construct a set (of naturals) $y \in \Delta^1_2$ such that $x \not \le_h y$, $y \not \le_h x$? What if we relax the condition so that we only require $y \not \le_h x$?