The degree of nonminimality is at most two

2022/06/27 by Freitag, James, Jaoui, Rémi, Moosa, Rahim · 3 citations
#03C45 #12H05 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2206.13450

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, a₁ and a₂, such that p has a nonalgebraic forking extension over A,a₁,a₂. Moreover, if A is contained in the field of constants then p already has a nonalgebraic forking extension over A,a₁. The results are also formulated in a more general setting.

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