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# Wydawnictwa / Czasopisma IMPAN / Fundamenta Mathematicae / Wszystkie zeszyty

## 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.

#### Autorzy

• Ziv ShamiDepartment of Mathematics and Computer Science
Ariel University, Samaria
44873 Ariel, Israel
e-mail

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