a1 Department of Mathematics, Monash University Clayton, Victoria 3168, Australia
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′.
(Received February 15 1988)
1980 Mathematics subject classification (Amer. Math. Soc.) (1985 Revision)
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