Is there a term for (Turing) degrees which realize the least possible jump (in the following sense) for the first n jumps.
That is degrees which satisfy for all $0 < m \leq n$:
$$X^m \equiv_T X \oplus 0^m$$
For n=1 this will obviously coincide with GL$_1$ but beyond that it will merely be contained in GL$_n$.
I feel like I've seen some term like sorta-generic or something for such degrees.
Part of the reason I'm asking is to search for some results about them for n greater than 1 so even if there is no term citations would be appreciated.
