On definable groups in real closed fields with a generic derivation, and related structures

Ya'acov Peterzil; Anand Pillay; Francoise Point

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arXiv · 2208.08293

On definable groups in real closed fields with a generic derivation, and related structures

Ya'acov Peterzil·Anand Pillay·Francoise Point

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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.

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BibTeX RIS

Ya'acov Peterzil, Anand Pillay, Francoise Point. 2022-08-17. On definable groups in real closed fields with a generic derivation, and related structures. https://arxiv.org/abs/2208.08293

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