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Representable Lexicographic Products

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Abstract

A linear ordering is said to be representable if it can be order-embedded into the reals. Representable linear orderings have been characterized as those which are separable in the order topology and have at most countably many jumps. We use this characterization to study the representability of a lexicographic product of linear orderings. First we count the jumps in a lexicographic product in terms of the number of jumps in its factors. Then we relate the separability of a lexicographic product to properties of its factors, and derive a classification of representable lexicographic products.

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References

  • Beardon, A. F., Candeal, J. C., Herden, G., Induráin, E. and Mehta, G. B. (2002) The non-existence of a utility function and the structure of non-representable preference relations, J. Math. Econom. 37, 17-38.

    Article  MATH  MathSciNet  Google Scholar 

  • Bridges, D. S. and Mehta, G. B. (1995) Representation of Preference Orderings, Springer, Berlin.

    Google Scholar 

  • Debreau, G. (1954) Representation of a preference ordering by a numerical function, In: R. Thrall, C. Coombs and R. Davies (eds), Decision Processes, Wiley, New York.

    Google Scholar 

  • Fleischer, I. (1961a) Numerical representation of utility, J. Soc. Indust. Appl. Math. 9(1), 48-50.

    Article  MATH  MathSciNet  Google Scholar 

  • Fleischer, I. (1961b) Embedding linearly ordered sets in real lexicographic products, Fund. Math. 49, 147-150.

    MATH  MathSciNet  Google Scholar 

  • Fishburn, P. C. (1968) Utility theory, Management Sci. 14(5), 335-378.

    Article  MATH  Google Scholar 

  • Giarlotta, A. (200?) The representability number of a chain, Topology Appl., to appear.

  • Knoblauch, V. (2000) Lexicographic orders and preference representation, J. Math. Econom. 34, 255-267.

    Article  MATH  MathSciNet  Google Scholar 

  • Kuhlmann, S. (1995) Isomorphisms of lexicographic powers of the reals, Proc. Amer. Math. Soc. 123(9), 2657-2662.

    Article  MATH  MathSciNet  Google Scholar 

  • Kunen, K. (1980) Set Theory. An Introduction to Independence Proofs, North-Holland, Amsterdam.

  • Rosenstein, J. G. (1982) Linear Orderings, Academic Press, New York.

    Google Scholar 

  • Wakker, P. (1988) Continuity of preference relations for separable topologies, Internat. Econom. Rev. 29(1), 105-110.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Illinois, Urbana, IL, 61801, USA

    Alfio Giarlotta

  2. Department of Economics and Quantitative Methods, University of Catania, Italy

    Alfio Giarlotta

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  1. Alfio Giarlotta
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Giarlotta, A. Representable Lexicographic Products. Order 21, 29–41 (2004). https://doi.org/10.1007/s11083-004-9308-3

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  • DOI: https://doi.org/10.1007/s11083-004-9308-3

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