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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