Completions of Pseudo Ordered Sets

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...

Full description

Saved in:
Bibliographic Details
Published inOrder (Dordrecht) Vol. 39; no. 1; pp. 95 - 111
Main Authors Cruz-Quinones, Maria D., Harding, John
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 2022
Springer Nature B.V
Subjects
Algebra
Discrete Mathematics
Lattices
Mathematics
Mathematics and Statistics
Order
Ordered Algebraic Structures
Pallets
Set theory
Pseudo order
Completion
Trellis
MacNeille completion
Online AccessGet full text

Cover

More Information
Summary: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 .
ISSN:0167-8094
1572-9273
DOI:10.1007/s11083-021-09565-4