具有有限群作用的微分场的模型论
Model theory of differential fields with finite group actions
摘要：
设G是有限群.利用微分场自同构研究了具有G作用的m个可换导子中特征为零的微分场类的模型论性质。在G-微分环的语言（即为导子和自同构添加符号的环的语言）中，我们证明了这个类有一个模型伴随表示的G-DCF.然后，我们部署在第一作者的论文[11]中开发的模型理论工具，以表明G-DCF的任何模型都是超简单的（但当G非平凡时不稳定），PAC微分场（因此在第二作者和Tressl [30]的意义上是微分大的），并且在添加一个参数元组后允许消除冗余。我们还讨论了有界PAC-微分场理论的模型完备性和超简单性（推广了Chatzidakis-Pillay [5]关于有界PAC-场的结果）。
英文摘要：
Let G be a finite group. We explore the model theoretic properties of the class of differential fields of characteristic zero in m commuting derivations equipped with a G-action by differential field automorphisms. In the language of G-differential rings (i.e. the language of rings with added symbols for derivations and automorphisms), we prove that this class has a model-companion - denoted G-DCF. We then deploy the model-theoretic tools developed in the first author's paper [11] to show that any model of G-DCF is supersimple (but unstable when G is nontrivial), a PAC-differential field (and hence differentially large in the sense of the second author and Tressl [30]), and admits elimination of imaginaries after adding a tuple of parameters. We also address model-completeness and supersimplicity of theories of bounded PAC-differential fields (extending the results of Chatzidakis-Pillay [5] on bounded PAC-fields).
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