  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.
