PFA and the positive ordinal partition relation

Determine whether the Proper Forcing Axiom implies the positive ordinal partition relation omega_1^2longrightarrow(omega_1^2,3)^2.

Background

The positive relation omega_12longrightarrow(omega_12,3)2 is a central ordinal partition problem. The paper records that Baumgartner posed the question of whether PFA implies this relation, but the paper does not resolve it; its forcing results instead concern preservation of existing negative witnesses and a model of a restricted sigma-centered form of Martin’s Axiom.

References

Baumgartner asked whether PFA implies eq:main-positive.

eq:main-positive:

2⟶(2,3)2.^2\longrightarrow(^2,3)^2.

— Martin's axiom and $ω_1^2 \longrightarrow (ω_1^2, 3)^2$  (2608.13213 - Golshani, 13 Aug 2026) in Section 1, Introduction