Geodesic
Boolean algebras of elementary characteristic (1,0,1) whose set of atoms and Ershov--Tarski ideal are computable
Algebra i logika, Tome 50 (2011) no. 2, pp. 133-151.

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It is proved that there exists a computable Boolean algebra of elementary characteristics (1,0,1) which has a computable set of atoms and a computable Ershov–Tarski ideal, but no strongly computable isomorphic copy. Also a description of $\Delta^0_6$-computable Boolean algebras is presented.
Keywords: Boolean algebra, computability, computable model. 
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M. N. Leontieva. Boolean algebras of elementary characteristic (1,0,1) whose set of atoms and Ershov--Tarski ideal are computable. Algebra i logika, Tome 50 (2011) no. 2, pp. 133-151. http://geodesic.mathdoc.fr/item/AL_2011_50_2_a0/

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