Shelah cardinal

In axiomatic set theory, Shelah cardinals are a kind of large cardinals. A cardinal <math>\kappa</math> is called Shelah iff for every <math>f:\kappa\rightarrow\kappa</math>, there exists a transitive class <math>N</math> and an elementary embedding <math>j:V\rightarrow N</math> with critical point <math>\kappa</math>; and <math>V_{j(f)(\kappa )}\subset N</math>.

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

References

• Ernest Schimmerling, Woodin cardinals, Shelah cardinals and the Mitchell-Steel core model, Proceedings of the American Mathematical Society 130/11, pp. 3385-3391, 2002, online

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