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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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