Geodesic
Decidable Boolean Algebras of Characteristic~$(1,0,1)$
Matematičeskie trudy, Tome 7 (2004) no. 1, pp. 3-12

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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. 
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P. E. Alaev. Decidable Boolean Algebras of Characteristic~$(1,0,1)$. Matematičeskie trudy, Tome 7 (2004) no. 1, pp. 3-12. http://geodesic.mathdoc.fr/item/MT_2004_7_1_a0/