A model-theoretic Baire category theorem for simple theories and its applications

Abstract

We prove a model theoretic Baire category theorem for τ f low-sets in a countable simple theory in which the extension property is firstorder and show some of its applications. We also prove a trichotomy for minimal types in countable nfcp theories: either every type that is internal in a minimal type is essentially-1-based by means of the forking topology or T interprets a strongly-minimal formula or T interprets an infinite definable 1-based group of finite D-rank.