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| | In [[axiomatic set theory]], '''Shelah cardinals''' are a kind of [[large cardinal]]s. A [[cardinal number|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 (set theory)|critical point]] <math>\kappa</math>; and <math>V_{j(f)(\kappa )}\subset N</math>. |
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| | A Shelah cardinal has a normal [[ultrafilter]] containing the set of [[weakly hyper-Woodin cardinal]]s below it. |
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| | == References == |
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| | * 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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| | {{settheory-stub}} |
| | [[Category:Large cardinals]] |
Revision as of 16:15, 21 November 2013
In axiomatic set theory, Shelah cardinals are a kind of large cardinals. A cardinal is called Shelah iff for every , there exists a transitive class and an elementary embedding with critical point ; and .
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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