We define a class \( \mathbb{K} \)Σ of primitive recursive structures whose existential diagram is decidable with primitive recursive witnesses. It is proved that a Boolean algebra has a presentation in \( \mathbb{K} \)Σ iff it has a computable presentation with computable set of atoms. Moreover, such a Boolean algebra is primitive recursively categorical with respect to \( \mathbb{K} \)Σ iff it has finitely many atoms. The obtained results can also be carried over to Boolean algebras computable in polynomial time.
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Supported by RFBR, project No. 17-01-00247.
Translated from Algebra i Logika, Vol. 57, No. 4, pp. 389-425, July-August, 2018.
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Alaev, P.E. Categoricity for Primitive Recursive and Polynomial Boolean Algebras. Algebra Logic 57, 251–274 (2018). https://doi.org/10.1007/s10469-018-9498-1
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DOI: https://doi.org/10.1007/s10469-018-9498-1