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Preprint Number 419
419. Artem Chernikov and Pierre Simon
Externally definable sets and dependent pairs II
Submission date: 14 February 2012.
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.
Mathematics Subject Classification: 03Cxx
Keywords and phrases: NIP, UDTFS, pairs, externally definable sets
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