Description:
Abstract In 1998 R. Downey formulated a problem: to describe a property $P$ of classical order types, which guarantees that if $\mathcal{L}$ is a low linear order and $P$ holds for the order type of $\mathcal{L}$ then $\mathcal{L}$ is isomorphic to a computable linear order. We find a new such property $P$. Also, we give an upper bound on a complexity of an isomorphism between computable and low copies and show that this bound is sharp.