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arXiv · 1504.01871

A definable henselian valuation with high quantifier complexity

Immanuel Halupczok·Franziska Jahnke
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Abstract

We give an example of a parameter-free definable henselian valuation ring which is neither definable by a parameter-free $\forall\exists$-formula nor by a parameter-free $\exists\forall$-formula in the language of rings. This answers a question of Prestel.

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Immanuel Halupczok, Franziska Jahnke. 2015-04-08. A definable henselian valuation with high quantifier complexity. https://arxiv.org/abs/1504.01871

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