Definable Groups in DCFA

2019/04/25 by Ronald F. Bustamante Medina, Medina, Ronald F. Bustamante
Computer Science · Mathematics · #11U09 #12H05 #12H10 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #FOS: Mathematics #Logic (math.LO) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1904.11586

openalex publication_date 2019/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

E. Hrushovski proved that the theory of difference-differential fields of characteristic zero has a model-companion. We denote it DCFA. In this paper we study definable groups in a model of DCFA. First we prove that such a group is embeds on an algebraic group. Then we study 1-basedeness, stability and stable embeddability of abelian definable groups.

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