, Volume 43, Issue 2, pp 73-87

Computable Homogeneous Boolean Algebras and a Metatheorem

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Abstract

We consider computable homogeneous Boolean algebras. Previously, countable homogeneous Boolean algebras have been described up to isomorphism and a simple criterion has been found for the existence of a strongly constructive (decidable) isomorphic copy for such. We propose a natural criterion for the existence of a constructive (computable) isomorphic copy. For this, a new hierarchy of \({\emptyset ^{(\omega )}} \) -computable functions and sets is introduced, which is more delicate than Feiner's. Also, a metatheorem is proved connecting computable Boolean algebras and their hyperarithmetical quotient algebras.