Measurable cardinal: Difference between revisions

Latest revision as of 01:32, 25 September 2014

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-In [[mathematics]], a [[cardinal number]] &kappa; is called '''superstrong''' [[if and only if]] there exists an [[elementary embedding]] ''j'' : ''V'' &rarr; ''M'' from ''V'' into a transitive inner model ''M'' with [[critical point (set theory)|critical point]] &kappa; and <math>V_{j(\kappa)}</math> &sube; ''M''.
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-Similarly, a cardinal κ is '''n-superstrong''' if and only if there exists an [[elementary embedding]] ''j'' : ''V'' &rarr; ''M'' from ''V'' into a transitive inner model ''M'' with [[critical point (set theory)|critical point]] &kappa; and <math>V_{j^n(\kappa)}</math> &sube; ''M''. [[Akihiro Kanamori]] has shown that the consistency strength of an n+1-superstrong cardinal exceeds that of an [[n-huge cardinal]] for each n > 0.
-== References ==
-* {{cite book|last=Kanamori|first=Akihiro|authorlink=Akihiro Kanamori|year=2003|publisher=Springer|title=The Higher Infinite : Large Cardinals in Set Theory from Their Beginnings|edition=2nd ed|isbn=3-540-00384-3}}
-[[Category:Set theory]]
-[[Category:Large cardinals]]
-{{settheory-stub}}

Measurable cardinal: Difference between revisions

Latest revision as of 01:32, 25 September 2014

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