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AN NIP-LIKE NOTION IN ABSTRACT ELEMENTARY CLASSES
Part of:
Model theory
Published online by Cambridge University Press: 25 September 2025
Abstract
This article is a contribution to the “neostability” type of result for abstract elementary classes. Under certain set theoretic assumptions, we propose a definition and a characterization of NIP in AECs. The class of AECs with NIP properly contains the class of stable AECs.1 We show that for an AEC K and 
$\lambda \geq LS(K)$, 
$K_\lambda $ is NIP if and only if there is a notion of nonforking on it which we call a w*-good frame. On the other hand, the negation of NIP leads to being able to encode subsets.
MSC classification
Primary:
03C45: Classification theory, stability and related concepts
03C48: Abstract elementary classes and related topics
Secondary:
03C52: Properties of classes of models
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- Copyright
- © The Author(s), 2025. Published by Cambridge University Press on behalf of The Association for Symbolic Logic
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