Decidable Boolean Algebras of Characteristic $(1,0,1)$

We prove that every 2-constructive Boolean algebra with elementary characteristic $(1,0,1)$ is strongly constructivizable (decidable). This completes the study of the relation between $n$-constructibility and strong constructibility for Boolean algebras of characteristics $(0,*,*)$ and $(1,*,*)$. In addition, we give a description for 3-constructive Boolean algebras by means of a $\Delta^0_2$-computable invariant.