Definable Utility in O-Minimal Structures

Representing binary ordering relations by numerical functions is a basic problem of the theory of measurement. We obtain definable utility representations for (both continuous and upper semicontinuous) definable preferences in o-minimal expansions of real closed ordered fields. Such preferences have particular significance for modeling 'bounded rationality'. The initial application of these ideas in economics was made by Blume and Zame. Our results extend their Theorem 1 in several directions.