A Mahlo cardinal (or strongly Mahlo cardinal) is an inaccessible cardinal \(\alpha\) such that the set of inaccessible cardinals below \(\alpha\) is a stationary subset of \(\alpha\) — that is, every closed unbounded set in \(\alpha\) contains an inaccessible cardinal (in which the Von Neumann definition of ordinals is used). The smallest Mahlo cardinal is sometimes called "the" Mahlo cardinal \(M\). (The eponym "Mahlo" has been appropriated as an adjective, so "\(\alpha\) is a Mahlo cardinal" may be rephrased as "\(\alpha\) is Mahlo," for example.)