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A characterization of finite Stone pseudocomplemented ordered sets. (English) Zbl 0863.06007
The main result is the following theorem. If \(S\) is a finite distributive and pseudocomplemented ordered set then \(S\) is Stone if and only if \(P\vee Q=S\) for every two different ideals \(P,Q\) of \(S\). \(S\) is Stone if for all \(a\in S\) the condition \(LU(a^*, a^{**})=S\) holds.

MSC:
06A99 Ordered sets
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