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Completions of Pseudo Ordered Sets

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Abstract

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.

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  1. New Mexico State University, Las Cruces, NM, USA

    Maria D. Cruz-Quinones & John Harding

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  1. Maria D. Cruz-Quinones
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  2. John Harding
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Correspondence to John Harding.

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Cruz-Quinones, M.D., Harding, J. Completions of Pseudo Ordered Sets. Order 39, 95–111 (2022). https://doi.org/10.1007/s11083-021-09565-4

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  • DOI: https://doi.org/10.1007/s11083-021-09565-4

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