\] 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 sequence $\langle \delta_\alpha\rangle_{\alpha<\kappa}\in\kappa^\kappa$ such that $\delta_0=0$, and $\delta_\alpha=\bigcup_{\beta<\alpha} \delta_\beta$ for limit $\alpha<\kappa$, there exists a sequence $\langle \eta_\alpha\rangle_{\alpha<\kappa}\in \kappa^\kappa$ such that for limit $\beta<\kappa$, $\