This article is cited in 11 papers

Computable Homogeneous Boolean Algebras and a Metatheorem

P. E. Alaev

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

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 $\varnothing^{(\omega)}$ – 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.

UDC: 512.563+510.5+510.6

Received: 23.04.2002

 English version: Algebra and Logic, 2004, 43:2, 73–87

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