Ax-Schanuel for linear differential equations

作者：Aslanyan Vahagn^*

来源：Archive for Mathematical Logic, 2018, 57(5-6): 629-648.

DOI：10.1007/s00153-017-0602-3

• Model-theoretic algebra
• Abstract differential equation
• Ax-Schanuel theorem
• Predimension
• Hrushovski construction

We generalise the exponential Ax-Schanuel theorem to arbitrary linear differential equations with constant coefficients. Using the analysis of the exponential differential equation by Kirby (The theory of exponential differential equations, 2006, Sel Math 15(3):445-486, 2009) and Crampin (Reducts of differentially closed fields to fields with a relation for exponentiation, 2006) 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.

• 出版日期2018-8