Let c denote the cardinality of the continuum. For ordinals α,β and a cardinal c, the 3-uniform ordinal Ramsey property α→(β,c)23 is defined as follows: for any 2-coloring of all 3-element subsets of the ordinal type α (where the coloring is given by a symmetric predicate on ordered triples of distinct elements), either there exists a subset s⊆α of order type β such that every 3-element subset of s is colored red, or there exists a subset s⊆α of cardinality c such that every 3-element subset of s is colored blue. Let ω denote the first infinite ordinal. Does the partition relation c→(ω⋅2,4)23 hold?