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Pseudo-trees and Boolean algebras. (English) Zbl 0778.06011

A partially ordered set \((T,\leq)\) is said to be a pseudo-tree if the initial segment \(\{x\in T:x\leq t\}\) of \(T\) is linearly ordered under \(\leq\) for every \(t\in T\). The authors consider Boolean algebras constructed in various ways from pseudo-trees and study the connection between pseudo-tree algebras and related classes of Boolean algebras.

MSC:

06E05 Structure theory of Boolean algebras
06E99 Boolean algebras (Boolean rings)
54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
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