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

Ziv Shami — 2013

Fundamenta Mathematicae

We prove a model-theoretic Baire category theorem for τ ̃ l o w 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.

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