Following the paper of the author, Zs. Nagy and W. Weiss [Period. Math. Hung. 10, 193-206 (1979; Zbl 0418.54019)], a \(T_ 3\) space X is called good (splendid) if it is countably compact, locally countable (and \(\omega\)-fair). \(G(\kappa)\) (resp. \(S(\kappa)\)) denotes the statement that a good (resp. splendid) space X with \(| X| =\kappa\) exists. We prove here that (i) \(Con(ZF)\to Con(ZFC+MA+2^{\omega}\) is \(big+S(\kappa)\) holds unless \(\omega =cf(\kappa)<\kappa)\); (ii) a supercompact cardinal implies \(Con(ZFC+MA+2^{\omega}>\omega_{\omega +1}+\neg G(\omega_{\omega +1}))\); (iii) the “Chang conjecture” \((\omega_{\omega +1},\omega_{\omega})\to (\omega_ 1,\omega)\) implies \(\neg S(\kappa)\) for all \(\kappa \geq \omega_{\omega}\); (iv) if \({\mathcal P}\) adds \(\omega_ 1\) dominating reals to V iteratively then, in \(V^{{\mathcal P}}\), we have \(G(\lambda^{\omega})\) for all \(\lambda\).