Let $S=\{\delta<\omega_2:\text{cf}(\delta)=\omega\}$. A well-known theorem of Shelah tells us that we can find $\langle C_\delta:\delta\in S\rangle$ such that
for every club $C\subseteq\omega_2$ there are stationarily many $\delta\in S$ with $C_\delta\subseteq C$, that is, $\langle C_\delta:\delta\in S\rangle$ is a type of *club-guessing sequence*.

Given $\sigma<\omega_1$, can we in ZFC find a club-guessing sequence as above so that the order-type of each $C_\delta$ is at least $\sigma$? Could we even demand that $C_\delta$ is of order-type $\delta$?

Note that we get such sequences $\langle C_\delta:\delta\in S\rangle$ if $\diamondsuit_S$ holds.