Woodin Cardinal
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High Quality Content by WIKIPEDIA articles! In set theory, a Woodin cardinal (named for W. Hugh Woodin) is a cardinal number such that for all functions f : there exists a cardinal with {f( ) } and an elementary embedding j : V M from V into a transitive inner model M with critical point and Vj(f)( ) M. An equivalent definition is this: is Woodin if and only if is strongly inaccessible and for all A subseteq V_lambda there exists a A which is -A-strong.

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High Quality Content by WIKIPEDIA articles! In set theory, a Woodin cardinal (named for W. Hugh Woodin) is a cardinal number such that for all functions f : there exists a cardinal with {f( ) } and an elementary embedding j : V M from V into a transitive inner model M with critical point and Vj(f)( ) M. An equivalent definition is this: is Woodin if and only if is strongly inaccessible and for all A subseteq V_lambda there exists a A which is -A-strong.