Rosenthal compacta and NIP formulas
Volume 231 / 2015
Fundamenta Mathematicae 231 (2015), 81-92
MSC: Primary 03C45; Secondary 54E52.
DOI: 10.4064/fm231-1-5
Abstract
We apply the work of Bourgain, Fremlin and Talagrand on compact subsets of the first Baire class to show new results about $\phi $-types for $\phi $ NIP. In particular, we show that if $M$ is a countable model, then an $M$-invariant $\phi $-type is Borel-definable. Also, the space of $M$-invariant $\phi $-types is a Rosenthal compactum, which implies a number of topological tameness properties.
