Submission date: 17 May 2023

Abstract:

We prove some results about the theory of independence in NSOP_3 theories that do not hold in NSOP_4 theories. We generalize Chernikov's work on simple and co-simple types in NTP_2 theories to types with NSOP_1 induced structure in N-ω-DCTP_2 and NSOP_3 theories, and give an interpretation of our arguments and those of Chernikov in terms of the characteristic sequences introduced by Malliaris. We then prove an extension of the independence theorem to types in NSOP_3 theories whose internal structure is NSOP_1. Additionally, we show that in NSOP_3 theories with symmetric Conant-independence, finitely satisfiable types satisfy an independence theorem similar to one conjectured by Simon for invariant types in NTP_2 theories, and give generalizations of this result to invariant and Kim-nonforking types.

Mathematics Subject Classification: 03C45

Keywords and phrases:

Full text arXiv 2305.09908: pdf, ps.