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The associated order of a preorder

Part of: Ordered sets

Published online by Cambridge University Press:  09 April 2009

John Boris Miller
John Boris Miller
Affiliation:
Department of Mathematics, Monash UniversityClayton, Victoria 3168, Australia
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Abstract

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Any preorder P on a set X has an associated preorder P′, P″, P‴, … The proerties of this sequence are studied. When X is finite the sequence is eventually periodic with period P = 1 or p = 1, the eventual constant preorder is full p = 2 the possible forms which the eventual alternating order can take are examined: first, the possible combinations of components are enumerated; second, the notion of ramification at a caste is used to show that X may in a heuristic sense be of unbounded complexity. If X is orderdense the periodicity starts at P′.

Keywords

preorderpartial orderassociated ordercasteramification.

MSC classification

Secondary: 06A99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 48 , Issue 1 , February 1990 , pp. 1 - 24
Copyright
Copyright © Australian Mathematical Society 1990

References

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