Abstract
Although it can be argued that, as far as the needs of economists are concerned, the problem of representing a preference relation by a real-valued utility function was solved by the work of Debreu [9,10] and others, the years since the publication of Debreu’s classic work “Theory of Value” have seen several significant new approaches to, and generalisations of, that problem [11–14].
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Reference
K.J. Arrow and F.H. Hahn, General Competitive Analysis, Oliver and Boyd, Edinburgh, 1971.
M.J. Beeson, Foundations of Constructive Mathematics, Ergebnisse der Math. und Ihrer Grenzgebiete, Folge 3, Bd. 6, Springer Verlag, Berlin.
Errett Bishop and. Douglas Bridges, Constructive Analysis, Grundlehren der math. Wissenschaften, Bd. 279, Springer Verlag, Berlin 1985.
D.S. Bridges, Preference and utility, a constructive development, J. Math. Econ. 9 (1982), 165–185.
D.S. Bridges, The constructive theory of preference relations on a locally compact space, to appear.
D.S. Bridges, A general constructive intermediate value theorem, to appear.
D.S. Bridges, Locatedness, convexity, and Lebesgue measurability,to appear in Quarterly J. Math.
D.S. Bridges and O. Demuth, Lebesgue measurability in constructive analysis, to appear.
G. Debreu, Theory of Value, John Wiley, New York, 1959.
G. Debreu, Continuity properties of Paretian utility, Int. Econ. Review 5 (1964), 285–293.
G. Mehta, Recent developments in utility theory, Indian Econ. J. 30 (1983), 103–124.
W. Neuefeind, On continuous utility, J. Econ. Theory 5 (1972), 174–176.
M.K. Richter, Continuous and semi-continuous utility, Int. Econ. Review 21 (1980), 293–299.
D. Sondermann, Utility representations for partial orders, J. Econ. Theory 23 (1980), 183–188.
I.D. Zaslayskii, Some properties of constructive real numbers and constructive functions, Trudy Math. Inst. Steklov 67 (1962), 385–457;
English translation in AMS Transi., Series 2, 57 (1966), 1–84.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1990 Plenum Press, New York
About this chapter
Cite this chapter
Bridges, D.S. (1990). Order Isomorphisms – A Constructive Measure-Theoretic View. In: Petkov, P.P. (eds) Mathematical Logic. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0609-2_16
Download citation
DOI: https://doi.org/10.1007/978-1-4613-0609-2_16
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4612-7890-0
Online ISBN: 978-1-4613-0609-2
eBook Packages: Springer Book Archive