An interval algebra is a Boolean algebra which is isomorphic to the algebra of finite unions of half-open intervals, of a linearly ordered set. An interval algebra is hereditary if every subalgebra is an interval algebra. We answer a question of M. Bekkali and S. Todorčević, by showing that it is consistent that every σ-centered interval algebra of size \(\mathfrak{b}\) is hereditary. We also show that there is, in ZFC, a hereditary interval algebra of cardinality ℵ₁.

中文翻译：

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遗传区间代数和连续基数特征

区间代数是布尔代数，它与线性序集的半开区间有限并集的代数同构。如果每个子代数都是区间代数，则区间代数是遗传的。我们证明M. Bekkali和S.Todorčević的问题是一致的，即每个大小为\（\ mathfrak {b} \）的σ中心间隔代数都是遗传的。我们还表明，在ZFC中，存在基数interval ₁的遗传间隔代数。