We prove a model-theoretic Baire category theorem for -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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm220-3-1,
author = {Ziv Shami},
title = {A model-theoretic Baire category theorem for simple theories and its applications},
journal = {Fundamenta Mathematicae},
volume = {220},
year = {2013},
pages = {191-206},
zbl = {1277.03034},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm220-3-1}
}
Ziv Shami. A model-theoretic Baire category theorem for simple theories and its applications. Fundamenta Mathematicae, Tome 220 (2013) pp. 191-206. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm220-3-1/