论文标题
具有有限群体行动的差分领域的模型理论
Model theory of differential fields with finite group actions
论文作者
论文摘要
令G为有限的组。我们探讨了通过差分磁场自动形态具有G-action的衍生衍生物中特征零差分差异场类别的模型理论特性。用g-差异戒指的语言（即带有衍生和自动形态符号的戒指的语言），我们证明该类具有模型兼容性 - 表示为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.我们还讨论了有界PAC差异字段的理论的模型完整性和超图（扩展了有界PAC场上的Chatzidakis-Pillay [5]的结果）。
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).
