 A set $A\subseteq 0^\kappa$ is here called [[**$\kappa$-T'-set**]{}]{} if there exists a sequence of cardinal numbers $\langle \lambda_\alpha\rangle_{\alpha<\kappa}\in\kappa^\kappa$ such that for every increasing sequence $\langle \delta_\alpha\rangle_{\alpha<\kappa}\in\kappa^\kappa$ 