A Simple definition of Mahlos

So called because the googology discord user “Simple” taught me it.

Basically, Iff for all functions f which map values in α to values in α, there is a regular β in α such that f maps values in β to values in β as well, α is weakly Mahlo. That is, α is weakly Mahlo iff all functions that are closed under α are also closed under some regular β which is in α.

Iff for all functions f which map values in α to values in α, there is a strongly inaccessible β in α such that f maps values in β to values in β as well, α is strongly Mahlo. That is, α is strongly Mahlo iff all functions that are closed under α are also closed under some inaccessible β which is in α.