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Pré-Publication, Document De Travail Année : 2012

Externally definable sets and dependent pairs II

Résumé

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.

Dates et versions

hal-00715373 , version 1 (06-07-2012)

Identifiants

Citer

Artem Chernikov, Pierre Simon. Externally definable sets and dependent pairs II. 2012. ⟨hal-00715373⟩
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