Computability of a topological poset

For subspaces X and Y of Q the notation X⩽hY means that X is homeomorphic to a subspace of Y and X∼Y means X⩽hY⩽hX. The resulting set P(Q)/∼ of equivalence classes is partially-ordered by the relation if X⩽hY. In a previous paper by the author it was established that this poset is essentially determined by considering only the scattered X⊆Q of finite Cantor–Bendixson rank. Results from that paper are extended to show that this poset is computable.