 It is easy to see that \(&lt;_m\) is a partial order on \(m\)-degrees—i.e., irreflexive, antisymmetric, and transitive. We accordingly introduce the structure \(\mathcal{D}_m = \langle \{\textrm{deg}_m(A) : A \subseteq \mathbb{N}\}, &lt;_m\rangle\) which is traditionally known as the many-one (or m-) degrees.