Abstract
In this paper, we discuss a version of Galois theory for systems of ordinary differential equations in which there is no fixed list of allowed transcendental operations. We prove a theorem saying that the field of integrals of a system of differential equations is equivalent to the field of rational functions on a hypersurface having a continuous group of birational automorphisms whose dimension coincides with the number of algebraically independent transcendentals introduced by integrating the system. The suggested construction is a development of the algebraic ideas presented by Paul Painleve in his Stockholm lectures.
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