Forking independence in differentially closed fields of positive characteristic

2025/11/07 by Piotr A. Kowalski, Omar León Sánchez, Kowalski, Piotr +3
Computer Science · Mathematics · #03C45 #03C60 #12F10 #12H05 #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.2511.04911

openalex publication_date 2025/11/07 · openalex created_date 2025/11/11 · openalex updated_date 2026/07/28

Abstract

We provide a differential-algebraic description of forking independence in the stable theory DCF_p,m of differentially closed fields of characteristic p>0 with m-many commuting derivations. As a by-product of this description, we prove that types over algebraically closed subsets of the real sort are stationary. In addition, we prove that the set of non-zero solutions to the Bernoulli differential equation x'=x^pk+1 with k>0 is strongly minimal and its geometry is strictly disintegrated, which implies that this set is algebraically independent over \mathbbF_p.

Citations

• Non-forking independence in stable theories
• Neostability transfers in derivation-like theories
• Stationarity and elimination of imaginaries in stable and simple theories
• Separably differentially closed fields
• PAC structures as invariants of finite group actions
• Operators coming from ring schemes
• Ax-Lindemann-Weierstrass with derivatives and the genus 0 Fuchsian\n groups
• Model theory of fields with free operators in positive characteristic
• Model theory of fields with free operators in characteristic zero
• Fields with several commuting derivations

Related

• Separably differentially closed fields
• Non-forking independence in stable theories
• Stable domination and independence in algebraically closed valued fields
• th-Forking, Algebraic Independence and Examples of Rosy Theories
• Fields with several commuting derivations