  We continue investigating the structure of externally definable sets in NIP
theories and preservation of NIP after expanding by new predicates. Most
importantly: types over finite sets are uniformly definable; over a model, a
family of non-forking instances of a formula (with parameters ranging over a
type-definable set) can be covered with finitely many invariant types; we give
some criteria for the boundedness of an expansion by a new predicate in a
distal theory; naming an arbitrary small indiscernible sequence preserves NIP,
while naming a large one doesn't; there are models of NIP theories over which
all 1-types are definable, but not all n-types.
