In mathematics, a Mahlo cardinal is a certain kind of large cardinal number. Mahlo cardinals were first described by Paul Mahlo (1911, 1912, 1913). As with all large cardinals, none of these varieties of Mahlo cardinals can be proved to exist by ZFC (assuming ZFC is consistent).
A cardinal number κ is called Mahlo if κ is inaccessible and the set U = {λ < κ: λ is inaccessible} is stationary in κ.
A cardinal κ is called weakly Mahlo if κ is weakly inaccessible and the set of weakly inaccessible cardinals less than κ is stationary in κ.
Read more about Mahlo Cardinal: Minimal Condition Sufficient For A Mahlo Cardinal, Example: Showing That Mahlo Cardinals Are Hyper-inaccessible, More Than Just Mahlo
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