Know Your Rank! (2512.18349v1)

Published 20 Dec 2025 in math.LO

Abstract: We study definable ranks of ordered fields, ordered abelian groups, and linear orders. For an arbitrary linear order $Γ$, we construct an ordered abelian group $G$ with archimedian spine $Γ$ and an ordered field $K$ with natural value group $G$ such that the definable ranks of $K$, $G$ and $Γ$ are all isomorphic. This answers a question of Krapp, Kuhlmann, and the second author.

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