Work

On differentiability in weakly o-minimal expansions of fields

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.03628

Authors: Acosta, Juan Pablo, Halevi, Yatir, Hasson, Assaf, Johnson, Will, Peterzil, Ya'acov

Language: English

Topic: Advanced Topology and Set Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7220464042

Cites: 2

Cited by:

Related to: 10