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On the Existence of Towers in Pseudo-Tree Algebras

机译：关于伪树代数中的塔的存在

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摘要

A tower in a Boolean algebra (BA) is a strictly increasing sequence, of regular order type, of elements of the algebra different from 1 but with sum 1. A pseudo-tree is a partially ordered set T such that the set T ↓ t = {s ∈ T : s < t] is linearly ordered for every t ∈ T. If that set is well-ordered, then T is a tree. For any pseudo-tree T, the BA Treealg(T) is the algebra of subsets of T generated by all of the sets T ↑ t = {s ∈ T : t ≤ s}. The main theorem of this note is a characterization in tree terms of when Treealg(T) has a tower of order type κ (given in advance).
机译：布尔代数（BA）中的塔是一个有序规则类型的，严格增长的序列，其代数元素不同于1但具有和1。伪树是部分有序集合T，使得集合T↓t = {s∈T：s

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