A model theoretic Baire category theorem for simple theories

Abstract

We prove a model theoretic Baire category theorem for ${\tilde{\tau }}_{low}^f$-sets in a countable simple theory in which the extension property is first-order 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 an infinite definable 1-based group of finite $D$-rank or $T$ interprets a strongly-minimal formula.