$\displaystyle S(A)\Leftrightarrow\forall f:\sup A\mapsto\sup A,\exists\alpha\in A,\forall\eta\in\alpha(f(\eta)\in\alpha)$
$\displaystyle\mathrm B(\alpha,\kappa)_0=\kappa\cup\{0,K\}$
$\displaystyle\mathrm B(\alpha,\kappa)_{n+1}=\{\gamma+\delta~|~\gamma,\delta\in\mathrm B(\alpha,\kappa)_n\}$
$\displaystyle\hphantom{\mathrm B(\alpha,\kappa)_{n+1}={}}{}\cup\{\Psi_\eta(\mu)~|~\mu\in\mathrm B(\alpha,\kappa)_n\land\eta\in\alpha\cap\mathrm B(\alpha,\kappa)_n\}$
$\displaystyle\mathrm B(\alpha,\kappa)=\bigcup_{n\in\mathbb N}\mathrm B(\alpha,\kappa)_n$