Lexicographic preference representation: Intrinsic length of linear orders on infinite sets

Vicki Knoblauch

Journal of Mathematical Economics, 2023, vol. 105, issue C

Abstract: The intrinsic length of a linear order is the minimum of all ordinals δ such that there is a binary-criteria lexicographic representation of the linear order in {0,1}δ. Assuming the Generalized Continuum Hypothesis, we show that, for each ordinal γ and infinite set X with cardinality κ, there exist a linear order on X such that γ is the intrinsic length of that linear order if and only if logκ≤γ≤κ. This intrinsic-length partition imposes a structure on the profusion of linear orders on an infinite set.

Keywords: Preference representation; Lexicographic order; Linear order; Ordinals; Cardinals (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:mateco:v:105:y:2023:i:c:s0304406823000162

DOI: 10.1016/j.jmateco.2023.102823

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