The theory of differentially closed fields (of characteristic zero) with n commuting derivations, DCF_0,n, is the model completion of the theory of differential fields of characteristic zero with n commuting derivations.

DCF_0,n is totally transcendental (as shown by Blum (for n = 1, McGrail, Pierce (after the others but with better axioms), and Yaffe (and more generally for Lie differential fields)) and the formula x = x has Lascar and Morley rank ωⁿ.

Hrushovski and Sokolovic showed that any strongly minimal set definable in DCF_0,1 satisfies the Zariski axioms, possibly after finitely many points are removed; and their proof generalizes immediately to any minimal set of finite differential dimension in DCF_0,n. Consequently, the trichotomy holds for strongly minimal sets in DCF_{0, n}.