Separation for non–self-preserving classes: MP+RRP without CBFA
Determine whether there exists, for a forcing class Γ that is never self-preserving, a model (for suitable κ and λ) in which the Σ_n maximality principle Σ_n–MP_Γ(H_κ) and the Σ_n residual reflection principle Σ_n–RRP(κ,λ,Γ) both hold while the bounded Σ_n-correct forcing axiom Σ_n–CBFA_{<κ}^{<λ}(Γ) fails.
References
Further open questions arise from the fact that, although the proof of Theorem \ref{thm:cbfafactor} does not appear to generalize beyond the provably self-preserving classes, it is unclear how to establish the separations that would definitively show that the theorem does not generalize: Is it consistent for suitable $\kappa$ that $\Sigma_n\mhyphen MP_\Gamma(H_\kappa)$ and $\Sigma_n\mhyphen RRP(\kappa, \lambda, \Gamma)$ hold but $\Sigma_n\mhyphen CBFA_{<\kappa}{<\lambda}(\Gamma)$ fails?