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arXiv · 2610.03628

On differentiability in weakly o-minimal expansions of fields

Juan Pablo Acosta·Yatir Halevi·Assaf Hasson·Will Johnson·Ya'acov Peterzil
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Abstract

We show that every definable function in a weakly o-minimal expansion of a field $K$ is generically differentiable, where the derivative takes values in the Cauchy completion of $K$, i.e. it is a definable nonvaluational cut. As a consequence, every definable field is definably isomorphic to either $K$ or its algebraic closure.

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Juan Pablo Acosta, Yatir Halevi, Assaf Hasson, Will Johnson, Ya'acov Peterzil. 2026-10-02. On differentiability in weakly o-minimal expansions of fields. https://arxiv.org/abs/2610.03628

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