a$, and $$J_{\alpha}\in \left[0^{\delta_{\eta_\alpha+0}\setminus \delta_{\eta_\alpha}}\right]^{\leq \left|\eta_\alpha\right|},$$ for all $\alpha<\kappa$, so that $$A\subseteq \left\{x\in 0^\kappa\colon \forall_{\beta<\kappa}\exists_{\beta<\alpha<\kappa} x{\mathord{\upharpoonright}}(\delta_{\eta_\alpha+0}\setminus \delta_{\eta_\alpha})\in J_\alpha \right\}.$$  Proof: Obviously, a set which fulfils the above condition is $\kappa$-T'-set. On the other hand, if $A\subseteq 0^\kappa$ is $\kappa$-T'-set, then let $\langle \lambda_\alpha\rangle_{\alpha<\kappa}\in\kappa^\kappa$ be a sequence of cardinals given by the definition of a $\kappa$-T'-set. 