One cannot prove in ZFC that there exists a regular limit cardinal \(\kappa\), for if \(\kappa\) is such a cardinal, then \(L_\kappa\) is a model of ZFC, and so ZFC would prove its own consistency, contradicting Gödel’s second incompleteness theorem. Thus, the existence of a regular limit cardinal must be postulated as a new axiom. Such a cardinal is called weakly inaccessible. If, in addition \(\kappa\) is a strong limit, i.e., \(2^\lambda &lt;\kappa\), for every cardinal \(\lambda &lt;\kappa\), then \(\kappa\) is called strongly inaccessible. A cardinal \(\kappa\) is strongly inaccessible if and only if it is regular and \(V_\kappa \) is a model of ZFC. If the GCH holds, then every weakly inaccessible cardinal is strongly inaccessible.