A model-theoretic Baire category theorem for simple theories and its applications
Tom 220 / 2013
Fundamenta Mathematicae 220 (2013), 191-206
MSC: Primary 03C45.
DOI: 10.4064/fm220-3-1
Streszczenie
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 topologies, or $T$ interprets an infinite definable 1-based group of finite $D$-rank or $T$ interprets a strongly minimal formula.
