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JAMDS
2002

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

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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.
Somdeb Lahiri
Added 22 Dec 2010
Updated 22 Dec 2010
Type Journal
Year 2002
Where JAMDS
Authors Somdeb Lahiri
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