Nonstandard utilities for lexicographically decomposable orderings

Rizza, Davide (2015) Nonstandard utilities for lexicographically decomposable orderings. Journal of Mathematical Economics, 60. 105–109. ISSN 0304-4068

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Abstract

Using a basic theorem from mathematical logic, I show that there are field-extensions of R on which a class of orderings that do not admit any real-valued utility functions can be represented by uncountably large families of utility functions. These are the lexicographically decomposable orderings studied in Beardon et al. (2002a). A corollary to this result yields an uncountably large family of very simple utility functions for the lexicographic ordering of the real Cartesian plane. I generalise these results to the lexicographic ordering of R^n, for every n > 2, and to lexicographic products of lexicographically decomposable chains. I conclude by showing how almost all of these results may be obtained without any appeal to the Axiom of Choice.

Item Type: Article
Additional Information: The following creative commons applies to the manuscript: https://creativecommons.org/licenses/by-nc-nd/3.0/
Uncontrolled Keywords: utility,lexicographic ordering,nonstandard analysis,economics, econometrics and finance(all),mathematics(all) ,/dk/atira/pure/subjectarea/asjc/2000
Faculty \ School: Faculty of Arts and Humanities > School of Politics, Philosophy, Language and Communication Studies
University of East Anglia > Faculty of Arts and Humanities > Research Groups > Philosophy
Depositing User: Pure Connector
Date Deposited: 20 Oct 2017 05:02
Last Modified: 23 Mar 2020 01:15
URI: https://ueaeprints.uea.ac.uk/id/eprint/65187
DOI: 10.1016/j.jmateco.2015.06.012

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