Jonathan Schilhan (University of Vienna)

Intermediate models and Kinna-Wagner degrees

The intermediate model theorem states that whenever G is generic over V and V ⊆ M ⊆ V[G] are models of ZFC, then M is also a forcing extension of V . Unfortunately, this fails completely if we only assume ZF instead. Can more can be said? The goal of our talk is to present a generalization of the above theorem that works for ZF and talk about some of the recent progress made in the theory of symmetric extensions. This is joint with A. Karagila.