Martin's axiom (MA) is a combinatorial principle that holds in many forcing extensions of set theory and has powerful consequences for cardinal arithmetic and partition relations. The paper studies whether MA implies that the ordinal omega_1 squared satisfies a particular Ramsey-type partition relation, meaning that for any two-coloring of pairs from omega_1 squared, one can find either a large monochromatic subset of order type omega_1 squared in the first color or a triple in the second color. The open problem is to determine the full landscape of which uncountable cardinals or ordinals satisfy analogous partition relations under MA or related forcing axioms, and specifically whether the methods used for omega_1 extend to larger cardinals like omega_2 or beyond.