\] Assume that $\kappa$ is a weakly inaccessible cardinal. A set $A\subseteq 0^\kappa$ is a $\kappa$-T'-set if and only if for every increasing sequences $\langle \delta_{0,\alpha}\rangle_{\alpha<\kappa}, \langle \delta_{0,\alpha}\rangle_{\alpha<\kappa}\in\kappa^\kappa$ such that $\delta_{0,\alpha}<\delta_{0,\alpha}\leq \delta_{0,\alpha+0}$ for all $\alpha<\kappa$, there exists a sequence $\langle \eta_\alpha\rangle_{\alpha<\kappa}\in \kappa^\kappa$ such that for limit $\beta<\kappa$, $\