Every ${\rm low}\sb 2$ Boolean algebra has a recursive copy

The degree of a structure $\mathcal{A}$ is the Turing degree of its open diagram $D(\mathcal{A})$, coded as a subset of $\omega$. Implicit in the definition is a particular presentation of the structure; the degree is not an isomorphism invariant. We prove that if a Boolean algebra $\mathcal{A}$ has a copy of ${\text{low}_2}$ degree, then there is a recursive Boolean algebra $\mathcal{B}$ which is isomorphic to $\mathcal{A}$. This builds on work of Downey and Jockusch, who proved the analogous result starting with a ${\text{low}_1}$ Boolean algebra.