When does NIP transfer from fields to henselian expansions?

Franziska Jahnke

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arXiv · 1607.02953

When does NIP transfer from fields to henselian expansions?

Franziska Jahnke

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Abstract

Let $K$ be an NIP field and let $v$ be a henselian valuation on $K$. We ask whether $(K,v)$ is NIP as a valued field. By a result of Shelah, we know that if $v$ is externally definable, then $(K,v)$ is NIP. Using the definability of the canonical $p$-henselian valuation, we show that whenever the residue field of $v$ is not separably closed, then $v$ is externally definable. In the case of separably closed residue field, we show that $(K,v)$ is NIP as a pure valued field.

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BibTeX RIS

Franziska Jahnke. 2016-07-11. When does NIP transfer from fields to henselian expansions?. https://arxiv.org/abs/1607.02953

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