Geodesic
Categoricity for primitive recursive and polynomial Boolean algebras
Algebra i logika, Tome 57 (2018) no. 4, pp. 389-425.

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We define a class $\mathbb K_\Sigma$ of primitive recursive structures whose existential diagram is decidable with primitive recursive witnesses. It is proved that a Boolean algebra has a presentation in $\mathbb K_\Sigma$ iff it has a computable presentation with computable set of atoms. Moreover, such a Boolean algebra is primitive recursively categorical with respect to $\mathbb K_\Sigma$ iff it has finitely many atoms. The obtained results can also be carried over to Boolean algebras computable in polynomial time.
Keywords: Boolean algebra, Boolean algebra computable in polynomial time, computable presentation, primitive recursively categorical Boolean algebra. 
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P. E. Alaev. Categoricity for primitive recursive and polynomial Boolean algebras. Algebra i logika, Tome 57 (2018) no. 4, pp. 389-425. http://geodesic.mathdoc.fr/item/AL_2018_57_4_a0/

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