Submission date: 8 November 2022

Abstract:

In this note, we prove that Kim-dividing over models is always witnessed by a coheir Morley sequence in NATP theories. Following the strategy of Chernikov and Kaplan, we obtain some corollaries which hold in NATP theories. Namely, (i) if a formula Kim-forks over a model, then it quasi-divides over the same model, (ii) for any tuple of parameters b and a model M, there exists a global coheir p containing tp(b/M) such that B and b are Kim-independent over M for all b|= p|MB.

Mathematics Subject Classification: 03C45

Keywords and phrases: Classification theory, Tree properties

Full text arXiv :2211.04213 pdf, ps.