MODEL THEORY OF DIFFERENTIAL FIELDS WITH FINITE GROUP ACTIONS

Daniel Max Hoffmann, Omar Leon Sanchez

Research output: Contribution to journalArticlepeer-review

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 (i.e. the language of rings with added symbols for derivations and automorphisms), we prove that this class has a modelcompanion – denoted G -DCF0,m. We then deploy the model-theoretic tools developed in the first author’s paper [13] to show that any model of G -DCF0,m 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 [33]), and admits elimination of imaginaries after adding a tuple of parameters. We also address model-completeness and supersimplicity of theories of bounded PACdifferential fields (extending the results of Chatzidakis-Pillay [5] on bounded PAC-fields).
Original languageEnglish
JournalJournal of Mathematical Logic
Publication statusAccepted/In press - 22 Sept 2021

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