Submission date: 31 August 2017

Abstract:

We prove that if T is a theory of large, bounded, fields of characteristic zero, with almost quantifier elimination, and T_D is the model companion of T + “D is a derivation”, then for any model U of T_D, and differential subfield K of U whose field of constants is a model of T, and linear differential equation DY = AY over K, there is a Picard-Vessiot extension L of K for the equation which is embedded in U over K Likewise for logarithmic differential equations over K on connected algebraic groups over the constants of K and the corresponding strongly normal extensions of K.

Mathematics Subject Classification: 12H05, 34M50, 03C10, 03C45

Keywords and phrases:

Full text arXiv 1709.00046: pdf, ps.