标题： 微分域上的模型理论与有限群作用 显示英文标题

标题： Model theory of differential fields with finite group actions

摘要： 设G为一个有限群。 我们探讨了在m个交换导数下特征为零的微分域类在G作用下的模型理论性质，该作用由微分域自同构实现。 在G-微分环的语言中（即，在环语言中添加导数和自同构符号的语言），我们证明了这个类有一个模型伴随 - 记作G-DCF。 然后，我们应用第一作者论文[11]中开发的模型论工具，证明任何G-DCF的模型都是超简单（但当G非平凡时是不稳定的），是一个PAC-微分域（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具有消除虚构的性质。 我们还讨论了有界PAC-微分域理论的模型完备性和超简单性（扩展了Chatzidakis-Pillay [5]关于有界PAC域的结果）。 显示英文摘要

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).