Charlotte Bartnick:
Stationarity in beautiful pairs
Zeit und Ort
Dienstag, 28.5.24, 14:30-15:30, Raum 404, Ernst-Zermelo-Str. 1
Zusammenfassung
A type in a stable theory \(T\) is stationary if it has a unique non-forking extension. By adding imaginary elements to a model of \(T\), types over algebraically closed sets in the expanded structure become stationary. If \(T\) does not eliminate imaginaries, the question arises whether types over algebraically closed subsets in the original model (real subsets) are also stationary.\n\nAfter reviewing all the above notions, we will discuss this problem for the theory \(T_P\) of beautiful pairs of models of a stable theory \(T\) introduced by Poizat. By a result of Pillay and Vassiliev, this theory does not have (geometric) elimination of imaginaries if an infinite group is definable in \(T\). We will prove that types over real algebraically closed sets in \(T_P\) are stationary.