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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     author = {M. N. Leontieva},
     title = {Boolean algebras of elementary characteristic (1,0,1) whose set of atoms and {Ershov{\textendash}Tarski} ideal are computable},
     journal = {Algebra i logika},
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     publisher = {mathdoc},
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     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2011_50_2_a0/}
}
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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/