Submission date: 27 June 2021

Abstract:

It is shown that if p is a complete type of Lascar rank at least 2 over A, in the theory of differentially closed fields of characteristic zero, then there exists a pair of realisations, a_1 and a_2, such that p has a nonalgebraic forking extension over A,a_1,a_2. Moreover, if A is contained in the field of constants then p already has a nonalgebraic forking extension over A,a_1. The results are also formulated in a more general setting.

Mathematics Subject Classification: 03C45, 12H05

Keywords and phrases:

Full text arXiv 2206.13450: pdf, ps.