TY - JOUR
T1 - S-forcing IIa
T2 - Adding diamonds and more applications: Coding sets, Arhangel'skii's problem and ℒ {Mathematical expression}
AU - Shelah, Saharon
AU - Stanley, Lee J.
AU - Burgess, John P.
PY - 1986/2
Y1 - 1986/2
N2 - 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, SK{lozenge, open}, of the forcing principle, SK{lozenge, open} of [20]. We obtain various applications of SK{lozenge, open}, to wit: the existence of a stationary subset of [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).
AB - 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, SK{lozenge, open}, of the forcing principle, SK{lozenge, open} of [20]. We obtain various applications of SK{lozenge, open}, to wit: the existence of a stationary subset of [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).
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U2 - 10.1007/BF02776239
DO - 10.1007/BF02776239
M3 - Article
AN - SCOPUS:51249178895
SN - 0021-2172
VL - 56
SP - 1
EP - 65
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 1
ER -