Effective definability of Kolchin polynomials

Freitag, James; León Sánchez, Omar; Li, Wei

doi:10.1090/proc/14869

Effective definability of Kolchin polynomials
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by James Freitag, Omar León Sánchez and Wei Li

Proc. Amer. Math. Soc. 148 (2020), 1455-1466

DOI: https://doi.org/10.1090/proc/14869

Published electronically: December 6, 2019

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Abstract:

While the natural model-theoretic ranks available in differentially closed fields (of characteristic zero), namely Lascar and Morley rank, are known not to be definable in families of differential varieties; in this note we show that the differential-algebraic rank given by the Kolchin polynomial is in fact definable. As a byproduct, we are able to prove that the property of being weakly irreducible for a differential variety is also definable in families. The question of full irreducibility remains open; it is known to be equivalent to the generalized Ritt problem.

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