A Strictly $ \text{NSOP}_3 $ Theory

We define the new notion of a $ \mu$-uniformly-counter-collapsed structure using which we introduce a theory $ \mathbb{T}_\mu $ serving as the first example of a strictly $ \text{NSOP}_3 $ theory. This answers a question posed in [DS04] and reappeared in [SU08] and [MS16]. The existence of such a theory provides a better understanding of the hierarchy of unstable theories without the strict order property.