Shelah cardinal

In axiomatic set theory, Shelah cardinals are a kind of large cardinals. A cardinal κ is called Shelah iff for every f : κ → κ , there exists a transitive class N and an elementary embedding j : V → N with critical point κ ; and V j ( f ) ( κ ) ⊂ N .

A Shelah cardinal has a normal ultrafilter containing the set of weakly hyper-Woodin cardinals below it.