Submission date: 7 March 2023

Abstract:

This paper is a contribution to “neo-stability” 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. We show that for an AEC K and λ ≥ LS(K), 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.

Mathematics Subject Classification: Primary: 03C45, 03C48. Secondary: 03C52

Keywords and phrases:

Full text arXiv 2303.04125: pdf, ps.