Submission date: 7 March 2011

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 a strongly-minimal formula or T interprets an infinite definable 1-based group of finite D-rank.

Mathematics Subject Classification: 03C45

Keywords and phrases: \tau^f-topology, \tilde\tau^f_{low}-sets, the extension property is first-order

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