Externally definable sets and dependent pairs II

By Artem Chernikov, Pierre Simon. 2012

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Author(s): Chernikov, A; Simon, P | Abstract: 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.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/3fbf227f8256c46396c87d6ea437a0afc80fdf78