Submission date: 17 August 2022

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.

Mathematics Subject Classification: 03C60, 03C64, 12H05, 14L10, 14P10

Keywords and phrases:

Full text arXiv 2208.08293: pdf, ps.