Equivalence of MM^{+ω1} and Σ_2–CMM

Determine whether Martin’s Maximum with ω1 many stationary set names (MM^{+ω1}) is equivalent to the Σ_2-correct stationary-set-preserving forcing axiom Σ_2–CMM.

Background

The paper presents several equivalent formulations of Σ_n–CFA and compares them to strengthened classical axioms like FA^{+}. Whether MM^{+ω1} coincides with Σ_2–CMM remains unsettled and would calibrate the exact strength of Σ_2–CMM relative to well-studied enhancements of MM.