The degree of nonminimality is at most 2

In this paper, it is shown that if p is an element of 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.

Automated summary

This paper demonstrates that in the theory of differentially closed fields of characteristic zero, if p is a complete type of Lascar rank at least 2 in S(A), then there exists a pair of realizations a(1), a(2) such that p has a nonalgebraic forking extension over Aa(1)a(2). Furthermore, 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.