Abstract
Using a basic theorem from mathematical logic, I show that there are fieldextensions of R on which a class of orderings that do not admit any realvalued 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.
Original language  English 

Pages (fromto)  105–109 
Journal  Journal of Mathematical Economics 
Volume  60 
Early online date  4 Jul 2015 
DOIs  
Publication status  Published  Oct 2015 
Keywords
 Utility
 Lexicographic ordering
 Nonstandard analysis
Profiles

Davide Rizza
 School of Politics, Philosophy, Language and Communication Studies  Associate Professor in Philosophy
 Philosophy  Member
Person: Academic, Teaching & Research