A simple proof of Suzumura's extension theorem for finite domains with applications

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.

• Type: Journal
• Year: 2002
• Where: JAMDS
• Authors: Somdeb Lahiri
• Keywords: Asymmetric Binary Relation, JAMDS 2002, Partial Orderings, Simple Proof