Weakly hyper-Woodin cardinal
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In axiomatic set theory, weakly hyper-Woodin cardinals are a kind of large cardinals. A cardinal κ is called weakly hyper-Woodin iff for every set S there exists a normal measure U on κ such that the set {λ < κ | λ is κ-S-strong} is in U.
The difference between hyper-Woodin cardinals and weakly hyper-Woodin cardinals is that the choice of U does not depend on the choice of the set S for hyper-Woodin cardinals.
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 (http://www.math.cmu.edu/~eschimme/papers/hyperwoodin.pdf)