To formulate the next stronger large-cardinal notion, let us say that a subset \(C\) of an infinite cardinal \(\kappa\) is closed if every limit of elements of \(C\) is also in \(C\); and is unbounded if for every \(\alpha &lt;\kappa\) there exists \(\beta\in C\) greater than \(\alpha\). For example, the set of limit ordinals less than \(\kappa\) is closed and unbounded. Also, a subset \(S\) of \(\kappa\) is called stationary if it intersects every closed unbounded subset of \(\kappa\). If \(\kappa\) is regular and uncountable, then the set of all ordinals less than \(\kappa\) of cofinality \(\omega\) is an example of a stationary set. A regular cardinal \(\kappa\) is called Mahlo if the set of strongly inaccessible cardinals smaller than \(\kappa\) is stationary. Thus, the first Mahlo cardinal is much larger than the first strongly inaccessible cardinal, as there are \(\kappa\)-many strongly inaccessible cardinals smaller than \(\kappa\).