Model Theory of Differentially Closed Fields with a Generic Automorphism

2009/07/23 by Ronald F. Bustamante Medina, Medina, Ronald F. Bustamante
Earth and Planetary Sciences · Mathematics · #Aquatic and Environmental Studies #math.AG #math.LO #msc:03C60 #msc:12L12 #msc:13L05

paper · pdf · doi:10.48550/arxiv.0907.3959

Doctoral thesis, advised by Zoe Chatzidakis

arxiv created 2009/07/23 · arxiv updated 2009/12/01

Abstract

E. Hrushovski proved tha the theory of difference-differential fields has a model companion. We prove this result and other maind properties of this theory that we call DCFA. We describe the SU rank a its relation with transcendence degree. We prove a version of Zilber's dichotomy and we give a description of Abelian definable groups.

Related

• The theory DCF_pA exists for p>0
• Zilber's Dichotomy for Differentially Closed Fields with an Automorphism
• Definable Groups in DCFA
• Model theory of differential fields with finite group actions
• Model theory, differential algebra and functional transcendence