is complete with respect to ( is 1-complete) if
- is recursively enumerable, and
- .
is complete with respect to ( is m-complete) if
- is recursively enumerable, and
- .
is 1-complete.
if is -complete, then isnt recursive.
the intuition behind such a proof would be that all -complete sets are reducible to each other, and if one of them was recursive all others would be recursive aswell by the-reducibility-1.