Consistency of lim^2 A_kappa at the continuum

Determine whether it is consistent with ZFC that lim^2 A_κ = 0 when κ = 2^{ℵ_0}, i.e., establish the consistency of the vanishing of the second derived limit of the inverse system A_κ at the cardinality of the continuum.

Background

Beyond the global question for all cardinals, the authors highlight a specific instance targeting κ equal to the continuum 2^{ℵ_0}. This focuses on the second derived limit, lim^2, whose behavior is known to have deep set-theoretic significance.

Achieving lim^2 A_{2^{ℵ_0}} = 0 would align with models where higher derived limits vanish, but the consistency of this particular case remains unsettled.