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Shelah cardinal

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Title: Shelah cardinal  
Author: World Heritage Encyclopedia
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Subject: List of Israeli inventions and discoveries, Large cardinals, List of large cardinal properties, Saharon Shelah, List of mathematical logic topics
Collection: Large Cardinals
Publisher: World Heritage Encyclopedia

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\rightarrow\kappa, there exists a transitive class N and an elementary embedding j:V\rightarrow 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.


  • 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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