# A model theoretic Baire category theorem for simple theories - Mathematics > Logic

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Abstract: We prove a model theoretic Baire category theorem for$\tilde\tau {low}^f$-sets in a countable simple theory in which the extensionproperty is first-order and show some of its applications. We also prove atrichotomy for minimal types in countable nfcp theories: either every type thatis internal in a minimal type is essentially-1-based by means of the forkingtopology or $T$ interprets an infinite definable 1-based group of finite$D$-rank or $T$ interprets a strongly-minimal formula.

Author: ** Ziv Shami**

Source: https://arxiv.org/