We define a class KΣ of primitive recursive structures whose existential diagram is decidable with primitive recursive witnesses. It is proved that a Boolean algebra has a presentation in KΣ iff it has a computable presentation with computable set of atoms. Moreover, such a Boolean algebra is primitive recursively categorical with respect to KΣ iff it has finitely many atoms. The obtained results can also be carried over to Boolean algebras computable in polynomial time.
- Boolean algebra
- Boolean algebra computable in polynomial time
- computable presentation
- primitive recursively categorical Boolean algebra