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Article
Mathematics
When any three solutions are independent
James Freitag et al.
Summary: Given an algebraic differential equation of order greater than one, 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. In the autonomous situation when the equation is over constant parameters the assumption that the order be greater than one can be dropped, and a nontrivial algebraic relation exists already between two solutions. These theorems are deduced as an application of a model-theoretic result, stating that a certain type is minimal if any three distinct realizations of it are independent.
INVENTIONES MATHEMATICAE (2022)
Article
Mathematics, Applied
Some model theory of fibrations and algebraic reductions
Rahim Moosa et al.
SELECTA MATHEMATICA-NEW SERIES (2014)