Mahlo cardinal ($\kappa \text{ Mahlo}$)

An inaccessible cardinal $\kappa$ whose inaccessible ordinals below it form a stationary set. Equivalently, every predicate expansion of $V_{\kappa }$ has an inaccessible elementary rank level below $\kappa$.

If $\kappa$ is Mahlo in $V$, then it is Mahlo in $L$. Inaccessibility is downward absolute, and every club in $L$ remains a club in $V$, where it meets a $V$-inaccessible ordinal.