Submission date: 28 August 2013.

Abstract:

We demonstrate existence and uniqueness of Picard--Vessiot extensions satisfying prescribed properties, for systems of linear differential equations over a field satisfying the same properties, under some closure assumptions on the field of constants. An example includes the case of a equations over a real field, with a real-closed field of constants. The result is obtained through a model theoretic approach.

Mathematics Subject Classification: 12H05, 12H20, 03C60

Keywords and phrases:

Full text arXiv 1308.6191: pdf, ps.