Externally definable sets and dependent pairs II
- Author(s): Chernikov, Artem
- Simon, Pierre
- et al.
Published Web Locationhttps://doi.org/10.1090/s0002-9947-2015-06210-2
© 2015 American Mathematical Society. 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.