PreprintCC BY 4.0arXiv
On differentiability in weakly o-minimal expansions of fields
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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BibTeX
@misc{acosta2026differentiability,
title = {{On differentiability in weakly o-minimal expansions of fields}},
author = {Juan Pablo Acosta and Yatir Halevi and Assaf Hasson and Will Johnson and Ya'acov Peterzil},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03628},
eprint = {2610.03628},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03628},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On differentiability in weakly o-minimal expansions of fields
AU - Juan Pablo Acosta
AU - Yatir Halevi
AU - Assaf Hasson
AU - Will Johnson
AU - Ya'acov Peterzil
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.03628
UR - https://arxiv.org/abs/2610.03628
AB - 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.
ER -