Work

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

Year: 2026

Type: article

Abstract: We study finite-dimensional groups definable in models of the theory RCF ∂ of real closed fields with a generic derivation (also known as CODF , the theory of closed ordered differential fields [28]). We prove that any such group Γ definably embeds in a “canonical” semialgebraic group G . We explain how our methods work in the general context of strongly model complete theories T of large “geometric” fields with a generic derivation, which includes the cases where T is the theory of pseudofinite fields and T = Th ( ℚ p ) . We also give a general theorem on recovering a definable group from generic data in the context of geometric theories. Finally we extend the methods to o -minimal theories with a generic derivation, due to Fornasiero and Kaplan, [10], and open theories of topological fields with a generic derivation, due to Cubides-Kovacsics and the third author, [7].

Source: Publications mathématiques de Besançon

DOI: 10.5802/pmb.68

Authors: Ya’acov Peterzil, Anand Pillay, Françoise Point

Institutions: University of Haifa, University of Notre Dame, University of Mons

Language: English

Topic: Advanced Topology and Set Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: National Science Foundation, Imperial College London, Fonds De La Recherche Scientifique - FNRS, Israel Science Foundation

Awards: FRG: Collaborative Research: Model Theory of Differential and Difference Equations with Applications, G1728871502, Topics in Model Theory, Topics in Model Theory, MFAI: Logic and the Theory of Neural Language Models