Abstract

In this paper, it is shown that if [Formula: see text] 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 [Formula: see text], [Formula: see text] such that p has a nonalgebraic forking extension over [Formula: see text]. Moreover, if A is contained in the field of constants then p already has a nonalgebraic forking extension over [Formula: see text]. The results are also formulated in a more general setting.