  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.

Commutative Algebra