AN NIP-LIKE NOTION IN ABSTRACT ELEMENTARY CLASSES
WENTAO YANG · Journal of Symbolic Logic · 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 lamda greater than or equals upper L upper S left parenthesis upper K right parenthesis $\lambda \geq LS(K)$ λ ≥ L S ( K ) , upper K Subscript lamda $K_\lambda $ K λ 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.