Abstract
Let X be a class, R a relation on X. Then R is said to be an order relation, ordering or order on X if it is reflexive, antisymmetric and transitive. So R is an order on X if and only if D X + R, R∩R-1 ∩ D X and R o R + R. An ordered set is an ordered pair (E,R) such that E is a set and R is an order on E. If the order R is clear from the context we may refer to the ordered set (E,R) simply as “the ordered set E”. Some authors prefer to use the term “partial order” for what we have called an order and instead of ordered sets speak of “partially ordered sets” or “posets”.
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© 1998 Springer Science+Business Media New York
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Adamson, I.T. (1998). Order Relations. In: A Set Theory Workbook. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8138-8_7
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DOI: https://doi.org/10.1007/978-0-8176-8138-8_7
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-0-8176-4028-6
Online ISBN: 978-0-8176-8138-8
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