Effective presentability of Boolean algebras of Cantor-Bendixson rank 1

We show that there is a computable Boolean algebra B and a computably enumerable ideal I of B such that the quotient algebra 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

Effective Presentability of Boolean Algebras of Cantor-Bendixson Rank 1

We show that there is a computable Boolean algebra B and a computably enumerable ideal I of B such that the quotient algebra 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