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2 Fundamenta Mathematicae

2 2013

2 Shami Z.

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

100%

Shami Z.

nr 3

191-206

We prove a model-theoretic Baire category theorem for $τ̃_{low}^f$-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.

On special partial types and weak canonical bases in simple theories

100%

Shami Z.

nr 1

1-6

We define the notion of a weak canonical base for a partial type in a simple theory. We prove that members of a certain family of partial types, which we call special partial types, admit a weak canonical base; this family properly contains the family of amalgamation bases.