Using filtrations between topologies, we present a general form of Scott analysis for definable equivalence relations. We develop a theory using this notion. We show that the speaker's canonical approximations of Polishable subgroups, Hjorth's Scott analysis of Polish group actions, and the Scott analysis in continuous model theory described by Doucha, Ben Yaacov, Nies, and Tsankov are special cases, appropriately understood, of our approach.

Parts of this work are joint with M. Lichman and J. Swaczyna.