“…We conclude this section by mentioning the exact big Ramsey degrees in the generic partial order in [2]. This result begins with the upper bounds proved by Hubička in [39] and then proceeds by taking a diagonal antichain D representing the generic partial order with additional structure of interesting levels built into D. A level ℓ of D is interesting if there are exactly two nodes, say s, t, in that level so that ( * ) for exactly one relation ρ ∈ {<, >, ⊥}, given any s ′ , t ′ ∈ D extending s, t, respectively, s ′ ρ t ′ , while there is no such relation for the pair s ↾ (ℓ − 1), t ↾ (ℓ − 1). Since an interesting level for a pair of nodes s, t predetermines the relations between any pair s ′ , t ′ extending s, t, respectively, passing numbers are unnecessary to the characterization.…”