Submission date: 15 March 2016

Abstract:

We show that the Ax-Schanuel theorem can be easily generalised to linear differential equations (with constant coefficients) of any order. Using the analysis of the exponential differential equation by J. Kirby and C. Crampin we give a complete axiomatisation of the first order theories of linear differential equations and show that the generalised Ax-Schanuel inequalities are adequate for them.

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

Keywords and phrases:

Full text arXiv 1603.04712: pdf, ps.