User blog comment:Rgetar/Higher weakly inaccessible and weakly Mahlo cardinals/@comment-28606698-20200106214759/@comment-32213734-20200107051651

> π is an uncountable regular cardinal iff every normal function f:π → π has a fixed point

Why? So every normal function on least uncountable cardinal Ω has a fixed point? Why?

> A cardinal π is weakly Mahlo iff every normal function on it has a regular fixed point

Can we replace "regular fixed point" with "regular limit" (that is f(x) for limit x) or just with "regular element"?

> f(κ)=κ and f(α)< κ for all α< κ

f(α)< f(κ) for all α< κ

Isn't that already in the definition of a normal function?