Towards an axiomatization of orderings
type: Item
instance of: scholarly article
title: Towards an axiomatization of orderings
zbMATH Open document ID: 0791.06001
DOI: 10.1007/BF00420357
author: Ton Storcken
author: Harrie de Swart
published in: Order
publication date: 1993-10-17T00:00:00Z
review text: The authors propose six criteria and claim that all well-known sets of specific orderings, such as linear and weak orderings, satisfy these six axioms. These criteria impose closeness of the set of relations with respect to permutation, conversion, concatenation, restriction and substitution. Further they study minimal extensions of a given set of relations which satisfy the axioms. They introduce a sufficient condition by which it is easy to check whether a set of relations is classifiably.
Mathematics Subject Classification ID: 06A05
Mathematics Subject Classification ID: 06A99
Mathematics Subject Classification ID: 06A06
zbMATH DE Number: 429195
zbMATH Keywords: ordering
zbMATH Keywords: axiomatization
zbMATH Keywords: closure properties
zbMATH Keywords: transitivity
zbMATH Keywords: weak orderings
zbMATH Keywords: minimal extensions of a given set of relations
MaRDI profile type: Publication
cites work: Collective rationality and dictatorship: The scope of the Arrow theorem
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cites work: Q5585195
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cites work: Note—A Preference Ranking Organisation Method
full work available at URL: https://doi.org/10.1007/bf00420357
OpenAlex ID: W2569299862
description: scientific article; zbMATH DE number 429195