Journal of the Australian Mathematical Society (Series A)

Table of Contents - 1990 - Volume 48, Issue 01  

Research Article

The associated order of a preorder

John Boris Millera1

a1 Department of Mathematics, Monash University Clayton, Victoria 3168, Australia

Abstract

Any preorder P on a set X has an associated preorder P′, P″, Pxs2034, … 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′.

(Received February 15 1988)

1980 Mathematics subject classification (Amer. Math. Soc.) (1985 Revision)

  • 06 A 99

Keywords and phrases

  • preorder;
  • partial order;
  • associated order;
  • caste;
  • ramification.