Submission date: 28 December 2020

Abstract:

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, we prove that this class has a model-companion - denoted GDCF. We then deploy the model-theoretic tools from [9] to show that any model of GDCF is supersimple (but unstable when G is nontrivial), a PAC-differential field (and hence differentially large in the sense of [27]), and admits elimination of imaginaries after adding a tuple of parameters. We also address model-completeness and simplicity of theories of bounded PAC-differential fields (extending the results in [5] for bounded PAC-fields).

Mathematics Subject Classification: 03C60 (Primary) 12L12, 12H05, 12H10 (Secondary)

Keywords and phrases: model theory, differential fields, difference fields, group actions

Full text arXiv 2012.14376: pdf, ps.