General factorization of Σ_n–CBFA into maximality and reflection principles

Establish whether, for a wide range of natural forcing classes Γ, the bounded Σ_n‑correct forcing axiom Σ_n–CBFA_{<κ}^{<λ}(Γ) is equivalent to the conjunction of an appropriate generalized maximality principle and a corresponding residual reflection principle.

Background

For provably self-preserving classes, the paper proves a factorization of Σn–CBFA into a Σ_n maximality principle over Hκ and a Σ_n residual reflection principle. Whether an analogous factorization extends broadly beyond self-preserving classes remains unsettled.