Computability of a topological poset

For subspaces X and Y of Q the notation X ⩽ h Y means that X is homeomorphic to a subspace of Y and X ∼ Y means X ⩽ h Y ⩽ h X . The resulting set P ( Q ) / ∼ of equivalence classes X ¯ = { Y ⊆ Q : Y ∼ X } is partially-ordered by the relation X ¯ ⩽ h Y ¯ if X ⩽ h Y . 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.