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This paper is a contribution to the problem of characterizing the K 0 -categorical Stone algebras. If the dense set is either finite or a chain, the problem is solved by reducing it to the Ko-categoricity of the skeleton and the dense set, solutions for these being known. If the dense set is a Boolean algebra, we show that this type of reduction works for certain subclasses but not for all such algebras. For generalized Post algebras the characterization problem is solved completely. Subjectdoi:10.1017/s1446788700011861 fatcat:fugjv52zpvhsja772gurpxnvbq