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Abstract

Chains of well-generated Boolean algebras whose union is not well-generated. (English summary) Israel J. Math. 154 (2006), 141–155. A Boolean algebra B is superatomic if every homomorphic image of B is atomic. This means that there is a Cantor-Bendixon derivative of B which is finite. A Boolean algebra is well-generated if there is a well-founded set of generators. The authors of the paper construct, by use of set-theoretical tools, two countable chains of superatomic and well-generated Boolean algebras, unions of which are not well-generated. The Boolean algebras constructed by them are of cardinality 2 ℵ0 with sets of atoms of cardinality of ℵ1. The question of whether the cardinalities are minimal is left open

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