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arXiv · 2501.10531

Growing Spines Ad Infinitum

Blaise Boissonneau·Anna De Mase·Franziska Jahnke·Pierre Touchard
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Abstract

We show that every non-trivial ordered abelian group $G$ is augmentable by infinite elements, i.e., we have $G\preccurlyeq H\oplus G$ for some non-trivial ordered abelian group $H$. As an application, we show that when $k$ is a field of characteristic 0, then $k$ is not $t$-henselian if and only if all henselian valuations with residue field $k$ are ($\emptyset$-)definable.

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Blaise Boissonneau, Anna De Mase, Franziska Jahnke, Pierre Touchard. 2025-01-17. Growing Spines Ad Infinitum. https://arxiv.org/abs/2501.10531

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