Jindrich Zapletal (University of Florida)

Fraenkel-Mostowski models revisited

A dynamical ideal is a group action on a set together with an ideal on the set which is invariant under the action. There is a permutation choiceless model of ZFA associated with each dynamical ideal. I will isolate several natural properties of dynamical ideals which translate into fragments of the Axiom of Choice in the permutation model. Verification of these properties leads to interesting problems in model theory, topology, and other fields, depending on the group action considered.