Ax-Schanuel for linear differential equations

Vahagn Aslanyan (Oxford)

Frank Adams 1,

I will give an introduction to the Ax-Schanuel property for 
differential equations and explain why it is relevant to model theory of 
differential fields. I will start with the classical Ax-Schanuel inequality for 
the exponential differential equation and generalise it to linear differential 
equations of any order with constant coefficients. Then I will give a complete 
axiomatisation of the first order theories of those equations and show that the 
generalised Ax-Schanuel inequalities are adequate for them.
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