Weak independence theorem for PAC structures

I would like to present several highlights from a current project with Junguk Lee. We are studying PAC substructures (e.g. existentially closed substructures) of some monster model of a stable theory and our goal is to describe such substructures with the Galois theory. It turns out that there is a possibility for defining independence relation in a saturated PAC substructure and this perspective independence relation descends from the absolute Galois group. Our results generalize a recent theorem of Zoe Chatzidakis.