Charlotte Bartnick:
On (non-)elimination of imaginaries
Zeit und Ort
Dienstag, 12.11.24, 14:30-15:30, Raum 404, Ernst-Zermelo-Str. 1
Zusammenfassung
Imaginaries are a way of introducing canonical representatives of equivalence classes. Given a theory, an important question is whether equivalence classes are already coded in the models of the theory so that one can avoid working with imaginaries (i.e. we say that the theory then eliminates imaginaries).\n\nIn this talk, we want to present a criterion that yields the failure of elimination of imaginaries due to equivalence classes that arise as cosets of subgroups. We will illustrate the main ideas by considering the example of the theory of beautiful pairs of algebraically closed fields. Pillay and Vassiliev proved that this theory does not have elimination of imaginaries. In this talk, we will present a different proof that generalizes to more theories of fields.