Geodesic
Computable Homogeneous Boolean Algebras and a Metatheorem
Algebra i logika, Tome 43 (2004) no. 2, pp. 133-158.

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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 $\varnothing^{(\omega)}$ – 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.
Keywords: computable homogeneous Boolean algebra, constructive copy for an algebra, hierarchy. 
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P. E. Alaev. Computable Homogeneous Boolean Algebras and a Metatheorem. Algebra i logika, Tome 43 (2004) no. 2, pp. 133-158. http://geodesic.mathdoc.fr/item/AL_2004_43_2_a0/

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