User blog comment:PolyhedralMatrix102/Question about Cardinals/@comment-11227630-20180317041140

Inaccessible cardinals are a kind of large cardinals. By definitions, they are uncountable (cardinality greater than $$\aleph_0$$), regular (cofinality equal to it) and strong limit (power set of all cardinals less than it still have cardinality less than it). The first inaccessible cardinal is so large that we can't get it from cardinals below it by normal operation on sets or cardinals, e.g. cardinal exponentiation, axiom of union, and axiom schema of replacement.

In googology, people use FGH to compare growth rate of functions, which uses ordinals. To represent large ordinals, one way is to use ordinal collapsing function (OCF), which uses large cardinals. Weakly inaccessible cardinals are more common in OCF than inaccessible cardinals. Weakly inaccessible cardinals, by definition, are uncountable, regular and limit (there is no greatest cardinal less than it).