Invariant types in NIP theories

Abstract

We study invariant types in NIP theories. Amongst other things: we prove a definable version of the (p,q)-theorem in theories of small or medium directionality; we construct a canonical retraction from the space of M-invariant types to that of M-finitely satisfiable types; we show some amalgamation results for invariant types and list a number of open questions.

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Cited by in corpus (10)

• Remarks on convergence of Morley sequences
• Density of compressible types and some consequences
• Glivenko-Cantelli classes and NIP formulas
• Around definable types in $p$-adically closed fields
• Weakly binary expansions of dense meet-trees
• Generic Stability and Modes of Convergence
• The definable (p,q)-theorem for distal theories
• Definable compactness in o-minimal structures
• The domination monoid in o-minimal theories
• Types, transversals and definable compactness in o-minimal structures