Effective Presentability of Boolean Algebras of Cantor-Bendixson Rank 1

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Journal of Symbolic Logic 64 (1):45-52 (1999)
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Abstract

We show that there is a computable Boolean algebra $\mathscr{B}$ and a computably enumerable ideal I of $\mathscr{B}$ such that the quotient algebra $\mathscr{B}/I$ is of Cantor-Bendixson rank 1 and is not isomorphic to any computable Boolean algebra. This extends a result of L. Feiner and is deduced from Feiner's result even though Feiner's construction yields a Boolean algebra of infinite Cantor-Bendixson rank.

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Computability and recursion.Robert I. Soare - 1996 - Bulletin of Symbolic Logic 2 (3):284-321.
Recursive and r.e. quotient Boolean algebras.John J. Thurber - 1994 - Archive for Mathematical Logic 33 (2):121-129.

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