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 [8], 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 coheirWe also show that in NATP theories, condition (ii) above is a necessary condition for being a witness coheir, assuming the existence of witnesses (see Definition 4.1 in this note). That is, if we assume that a witness coheir for Kim-dividing always exists over any given model, then a coheir p ⊇ tp(a/M ) must satisfy (ii) whenever it is a witness for Kim-dividing of a over a model M . We also give a sufficient condition for the existence of witness coheirs in terms of pre-independence relations.At the end of the paper, we leave a short remark on Mutchnik's recent work [16]. We point out that in ω-NDCTP 2 theories, a subclass of the class of NATP theories, Kim-forking and Kim-dividing are equivalent over models, where Kim-dividing is defined with respect to invariant Morley sequences, instead of coheir Morley sequences as in [16].
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