Nonstandard utilities for lexicographically decomposable orderings

Rizza, Davide ORCID: https://orcid.org/0000-0002-1375-371X (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 (former - to 2024)
UEA Research Groups:	Faculty of Arts and Humanities > Research Groups > Philosophy Faculty of Science > Research Groups > Algebra, Logic & Number Theory
Depositing User:	Pure Connector
Date Deposited:	20 Oct 2017 05:02
Last Modified:	11 Nov 2024 09:30
URI:	https://ueaeprints.uea.ac.uk/id/eprint/65187
DOI:	10.1016/j.jmateco.2015.06.012

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