We apply the work of Bourgain, Fremlin and Talagrand on compact subsets of the first Baire class to show new results about ϕ-types for ϕ NIP. In particular, we show that if M is a countable model, then an M-invariant ϕ-type is Borel-definable. Also, the space of M-invariant ϕ-types is a Rosenthal compactum, which implies a number of topological tameness properties.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm231-1-5,
author = {Pierre Simon},
title = {Rosenthal compacta and NIP formulas},
journal = {Fundamenta Mathematicae},
volume = {228},
year = {2015},
pages = {81-92},
zbl = {06451633},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm231-1-5}
}
Pierre Simon. Rosenthal compacta and NIP formulas. Fundamenta Mathematicae, Tome 228 (2015) pp. 81-92. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm231-1-5/