A pseudo ordered set (X,≤) is a set X with a binary relation ≤ that is reflexive and antisymmetric. We associate to a pseudo ordered set X, a partially ordered set Γ(X) called the covering poset. Taking any completion (C,f) of the covering poset Γ(X), and a special equivalence relation 𝜃 on this completion, yields a completion C/𝜃 of the pseudo ordered set X. The case when (C,f) is the MacNeille completion of Γ(X) gives the pseudo MacNeille completion of X.

中文翻译：

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伪有序集的完成

伪有序集（X，≤）是自反和反对称的二元关系≤的集X。我们将其与伪有序集X关联，后者是称为覆盖姿态的部分有序集Γ（X）。采取任何完成（Ç，˚F覆盖偏序集Γ（的）X），和一个特殊的等价关系θ在此完成时，产生一个完成ç / θ伪的有序集合X。当的情况下（Ç，˚F）是Γ（的麦克尼尔完成X）给出的伪麦克尼尔完成X。