# When any three solutions are independent

@inproceedings{Freitag2021WhenAT, title={When any three solutions are independent}, author={James Freitag and R'emi Jaoui and Rahim Moosa}, year={2021} }

Given an algebraic differential equation of order > 1, it is shown that if there is any nontrivial algebraic relation amongst any number of distinct nonalgebraic solutions, along with their derivatives, then there is already such a relation between three solutions. This is deduced as an application of the following model-theoretic result: Suppose p is a stationary nonalgebraic type in the theory of differentially closed fields of characteristic zero; if any three distinct realisations of p are…

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