Mahlo cardinal

Summary

A Mahlo cardinal is an inaccessible cardinal $\kappa$ such that the inaccessible cardinals below $\kappa$ form a stationary set in $\kappa$. So a Mahlo cardinal has very many inaccessible cardinals below it, and it is the $\kappa$-th inaccessible cardinal. The notion is named after Paul Mahlo. Mahlo cardinals are stronger than inaccessible cardinals, and weaker than weakly compact cardinals.