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arXiv · 2512.18349

Know Your Rank!

Blaise Boissonneau·Lasse Vogel
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Abstract

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

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Blaise Boissonneau, Lasse Vogel. 2025-12-20. Know Your Rank!. https://arxiv.org/abs/2512.18349

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