Michael Lösch:
On the canonical base property and transfer of internality
Zeit und Ort
Dienstag, 7.12.21, 14:30-15:30, Raum 404, Ernst-Zermelo-Str. 1
Zusammenfassung
Baldwin and Lachlan proved that an uncountably categorical structure is largely controlled by a strongly minimal set D and the Canonical Base Property (CBP) states that over a realization of a stationary type, its canonical base is always almost internal to the strongly minimal set D.\nChatzidakis, Moosa and Pillay showed under the assumption of the CBP that every almost D-internal type transfers internality on intersections and more generally on quotients. Both properties do not hold in the uncountably categorical structure without the CBP, produced by Hrushovski, Palacín and Pillay.\n\nIn this talk, I will show that transfer of internality of quotients already implies the CBP and present the counter-example to the CBP as an additive cover of the complex numbers. In order to show that this structure does not transfer internality, we must consider imaginary elements (definable equivalence classes) and obtain a connection between elimination of finite imaginaries and the failure of the CBP.