A simple proof of Suzumura's extension theorem for finite domainswith applications
[摘要] In this paper we provide a simple proof of the extension theorem for partialorderings due to Suzumura [1983] when the domain of the partial order is finite.The extension theorem due to Szpilrajn [1930] follows from this theorem. Szpilrajnsextension theorem is used to show that an asymmetric binary relation is contained inthe asymmetric part of a linear order if and only if it is acyclic. This theorem is thenapplied to prove three results. Finally we introduce the concept of a threshold choicefunction, and our third result says that such choice functions are the only ones to satisfya property called functional acyclicity.
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[效力级别] [学科分类] 自然科学(综合)
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