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arXiv · 2206.13450

The degree of nonminimality is at most two

James Freitag·Rémi Jaoui·Rahim Moosa
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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.

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James Freitag, Rémi Jaoui, Rahim Moosa. 2022-06-27. The degree of nonminimality is at most two. https://arxiv.org/abs/2206.13450

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