Global square

Global square is an important concept in set theory, a branch of mathematics. Define Sing to be the class of all limit ordinals which are not regular. Global square states that there is a system $(C_\beta)_{\beta \in Sing}$ satisfying:

$C_\beta$ is a club set of $\beta$ .
ot $(C_\beta) < \beta$
If $\gamma$ is a limit point of $C_\beta$ then $\gamma \in Sing$ and $C_\gamma = C_\beta \cap \gamma$