Model theory of fields with free operators in characteristic zero

2012/12/23 by Moosa, Rahim, Scanlon, Thomas · 4 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics #Logic (math.LO) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1212.5838

Abstract

Generalising and unifying the known theorems for difference and differential fields, it is shown that for every finite free \mathbb S-algebra \mathcal D over a field A of characteristic zero the theory of \mathcal D-fields has a model companion \mathcal D-CF₀ which is simple and satisfies the Zilber dichotomy for finite-dimensional minimal types.

Cited by

• Dimension Polynomials for Affine Partial Difference Algebraic Groups
• Forking independence in differentially closed fields of positive characteristic
• Embedding stable groups into algebraic groups
• Generic derivations on algebraically bounded structures II Model theoretical properties

Related

• The model companion of differential fields with free operators
• The uniform companion for fields with free operators in characteristic zero
• Model theory of fields with free operators in positive characteristic
• On the model companion of partial differential fields with an\n automorphism
• Zilber dichotomy for DCF_0,m