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Given two algebraic ODEs, is there a differential-algebraic relation between generic tuples of their solutions? In recent work with Freitag and Moosa, we produce a bound on the length of tuples one must look at to f ind a relation. Our proof relies on two ingredients. The first is differential Galois theory, combined with the recent proof by Freitag and Moosa of the Borovik-Cherlin conjecture in algebraically closed fields. The second is some general model theory result which allows us to factor any relation through some minimal ODE. I will give a precise statement of our result and sketch the proof. I will also explain why our bound is tight.
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Given two algebraic ODEs, is there a differential-algebraic relation between generic tuples of their solutions? In recent work with Freitag and Moosa, we produce a bound on the length of tuples one must look at to f ind a relation. Our proof relies on two ingredients. The first is differential Galois theory, combined with the recent proof by Freitag and Moosa of the Borovik-Cherlin conjecture in algebraically closed fields. The second is some ...
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03C45 ; 14L30 ; 12H05 ; 12L12