Journal of Applied Mathematics and Decision Sciences
Volume 6 (2002), Issue 3, Pages 183-190
doi:10.1155/S1173912602000111
Abstract
In this paper we provide a simple proof of the extension theorem for partial
orderings due to Suzumura [1983] when the domain of the partial order is finite.
The extension theorem due to Szpilrajn [1930] follows from this theorem. Szpilrajns
extension theorem is used to show that an asymmetric binary relation is contained in
the asymmetric part of a linear order if and only if it is acyclic. This theorem is then
applied to prove three results. Finally we introduce the concept of a threshold choice
function, and our third result says that such choice functions are the only ones to satisfy
a property called functional acyclicity.