S-forcing IIa: Adding diamonds and more applications: Coding sets, Arhangel'skii's problem and ℒ {Mathematical expression}

We continue our earlier paper [20] by proving the equivalence, for regular κ>ω, of the existence of (κ, 1) morasses with built-in {black diamond suit} sequences and a strengthening, S_K{lozenge, open}, of the forcing principle, S_K{lozenge, open} of [20]. We obtain various applications of S_K{lozenge, open}, to wit: the existence of a stationary subset of [K₊]_<K with sup as coding function, the existence of a counterexample to Arhangel'skii's conjecture (κ=א₁) and compactness, axiomatizability and transfer properties for the Magidor-Malitz language ℒ {Mathematical expression} (κ=א₁).