Externally definable sets and dependent pairs II

2012/02/13 by Chernikov, Artem, Simon, Pierre · 1 citation
#03Cxx #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1202.2650

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.

Cited by

• Model theory of difference fields with an additive character on the fixed field

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• Definable and invariant types in enrichments of NIP theories
• On uniform definability of types over finite sets for NIP formulas
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• Characterizations of monadic NIP
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