Apparaît dans la collection : 2018 - T1 - WS3 - Model theory and applications

This is joint work with Piotr Kowalski. A G-field is a field, together with an acion of a group G by field automorphisms. If an axiomatization for the class of existentially closed G-fields exists we call the resulting theory G-TCF. If G is the group of integers then G-TCF exists and coincides with ACFA. More generally when G is free on n-generators then the theory of existentially closed models is ACFAn. G-TCF also exists when G is finite. Our main theorem says that G-TCF exists when G is virtually free. We also give criteria for the simplicity of G-TCF.