Abstract
Within the frames of the Σ-definability approach propounded by Yu. L. Ershov, we study into the definability of Boolean algebras and their Frechet ranks in hereditarily finite superstructures. Examples are constructed of a superatomic Boolean algebra whose Frechet rank is not Σ-definable in the hereditarily finite superstructure over that algebra, and of an admissible set in which the atomless Boolean algebra is not autostable.
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