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• W2033713905 abstract "A well-known result in the theory of binary relations states that a binary relation has a complete and transitive extension if and only if it is consistent ([Suzumura K., 1976. Remarks on the theory of collective choice, Economica 43, 381–390], Theorem 3). A relation is consistent if the elements in the transitive closure are not in the inverse of the asymmetric part. We generalize this result by replacing the transitive closure with a more general function. Using this result, we set up a procedure which leads to existence results for complete extensions satisfying various additional properties. We demonstrate the usefulness of this procedure by applying it to the properties of convexity, homotheticity and monotonicity." @default.
• W2033713905 created "2016-06-24" @default.
• W2033713905 creator A5016639671 @default.
• W2033713905 date "2009-01-01" @default.
• W2033713905 modified "2023-10-18" @default.
• W2033713905 title "A general extension result with applications to convexity, homotheticity and monotonicity" @default.
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• W2033713905 doi "https://doi.org/10.1016/j.mathsocsci.2008.08.005" @default.
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