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arXiv · 1706.03376

Strongly Dependent Ordered Abelian Groups and Henselian Fields

Yatir Halevi·Assaf Hasson
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Abstract

Strongly dependent ordered abelian groups have finite dp-rank. They are precisely those groups with finite spines and $|\{p\text{ prime}:[G:pG]=\infty\}|<\infty$. We apply this to show that if $K$ is a strongly dependent field, then $(K,v)$ is strongly dependent for any henselian valuation $v$.

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Yatir Halevi, Assaf Hasson. 2017-06-11. Strongly Dependent Ordered Abelian Groups and Henselian Fields. https://arxiv.org/abs/1706.03376

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