Definable Utility in O-Minimal Structures

Thumbnail Image

View/Download File

Persistent link to this item

View Statistics

Journal Title

Journal ISSN

Volume Title


Definable Utility in O-Minimal Structures

Published Date



Center for Economic Research, Department of Economics, University of Minnesota


Working Paper


Representing binary ordering relations by numerical functions is a basic problem of the theory of measurement. It has applications in many fields of science, and arises in psychology and economics as the problem of establishing utility functions for preference relations. 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" [18]. Our proofs are based on geometric theorems for definable sets, and provide new alternatives to the classical tools of separability (Debreu [5], Rader [16]) and metric-completeness (Arrow and Hahn [1]). The initial application of these ideas in economics was made by Blume and Zame (1992). Our results extend their Theorem 1 in several directions (see Remark la below).


Related to



Series/Report Number

Funding information

Isbn identifier

Doi identifier

Previously Published Citation

Richter, M.K. and Wong, K., (1996), "Definable Utility in O-Minimal Structures", Discussion Paper No. 296, Center for Economic Research, Department of Economics, University of Minnesota.

Suggested citation

Richter, Marcel K.; Wong, Kam-Chau. (1996). Definable Utility in O-Minimal Structures. Retrieved from the University Digital Conservancy,

Content distributed via the University Digital Conservancy may be subject to additional license and use restrictions applied by the depositor. By using these files, users agree to the Terms of Use. Materials in the UDC may contain content that is disturbing and/or harmful. For more information, please see our statement on harmful content in digital repositories.