Simple-like independence relations in abstract elementary classes

We introduce and study simple supersimple independence relations in the context of AECs with a monster model. Theorem 0.1Let K be an AEC model.•If has relation, then does not have 2-tree property.•If relation (<?0)-witness property for singletons, tree property. 0.1 Let If The proof both facts is done by finding cardinal bounds to classes small Galois-types over fixed model that are inconsistent large subsets. think this finer way counting types interesting notion itself. characterize finiteness Lascar rank under locality assumptions on relation.