Shelah cardinal

Shelah cardinal

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

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, [http://www.math.cmu.edu/~eschimme/papers/hyperwoodin.pdf online]


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