Consistency of cf(cov(E)) = ω

Determine whether it is consistent with ZFC that the cofinality of the covering number of the ideal E (the ideal generated by F_sigma Lebesgue measure–zero subsets of R) is ω, i.e., establish Cons(ZFC ⊢ cf(cov(E)) = ω).

Background

The ideal E is generated by F_sigma subsets of the real line that have Lebesgue measure zero. Its covering number cov(E) is the minimal cardinality of a family in E whose union is R. While Shelah proved that cf(cov(N)) = ω is consistent with ZFC, the analogous question for E remains unresolved.

The notes explain that a positive solution would require forcing d < cov(E), which entails cov(E) = cov(N); hence one would need an ω^ω-bounding forcing that yields cf(cov(N)) = ω.