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

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arxiv 2208.08293 v2 pith:PCKWVA6W submitted 2022-08-17 math.LO

Ya'acov Peterzil , Anand Pillay , Francoise Point This is my paper
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Externally definable fsg groups in NIP theories

    math.LO 2025-06 accept novelty 8.0 of 10

    Every fsg group externally definable in an NIP structure is definably isomorphic to a group interpretable in that structure.

  2. Generic derivations on algebraically bounded structures II. Model theoretical properties

    math.LO 2025-07 conditional novelty 6.0 of 10

    The model completion of an algebraically bounded field theory with generic derivations inherits simplicity and related tameness properties, and is totally transcendental exactly when the base theory is ACF0 and the de...

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