Shelah cardinal

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

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

[edit] 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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