On definable groups in real closed fields with a generic derivation, and related structures
Abstract
We study finite-dimensional groups definable in models of the theory of real closed fields with a generic derivation (also known as CODF). We prove that any such group definably embeds in a semialgebraic group. We extend the results to several more general contexts; strongly model complete theories of large geometric fields with a generic derivation, model complete o-minimal expansions of RCF with a generic derivation, open theories of topological fields with a generic derivation. We also give a general theorem on recovering a definable group from generic data in the context of geometric structures.
Cite
@article{arxiv.2208.08293,
title = {On definable groups in real closed fields with a generic derivation, and related structures},
author = {Ya'acov Peterzil and Anand Pillay and Francoise Point},
journal= {arXiv preprint arXiv:2208.08293},
year = {2023}
}
Comments
41 pages. Many corrections made from the first version, and new references to related works are mentioned in the introduction. The title is slightly changed