 A set $A\subseteq 0^\kappa$ is a $\kappa$-T'-set if and only if there exists a sequence of cardinal numbers $\langle \lambda_\alpha\rangle_{\alpha<\kappa}\in\kappa^\kappa$ such that for every increasing sequences $\langle \delta_{0,\alpha}\rangle_{\alpha<\kappa}, \langle \delta_{0,\alpha}\rangle_{\alpha<\kappa}\in\kappa^\kappa$