The degree of nonminimality is at most 2

Abstract

. It is shown that if p ∈ S ( A ) is a complete type of Lascar rank at least 2, in the theory of differentially closed fields of characteristic zero, then there exists a pair of realisations a 1 ,a 2 such that p has a nonalgebraic forking extension over Aa 1 a 2 . Moreover, if A is contained in the field of constants then p already has a nonalgebraic forking extension over Aa 1 . The results are also formulated in a more general setting.