Woodin cardinal

GPTKB entity

Statements (23)
Predicate Object
gptkbp:instanceOf large cardinal
gptkbp:category cardinal number
set theory concept
gptkbp:consistencyStrength stronger than measurable cardinal
weaker than supercompact cardinal
gptkbp:defines A cardinal κ is Woodin if for every function f:κ→κ there is a cardinal λ<κ such that f''λ⊆λ and there is an elementary embedding j:V→M with critical point λ and V_{j(f)(λ)}⊆M.
gptkbp:field gptkb:set_theory
gptkbp:firstAppearance 1980s
https://www.w3.org/2000/01/rdf-schema#label Woodin cardinal
gptkbp:implies measurable cardinal
gptkbp:introduced gptkb:W._Hugh_Woodin
gptkbp:namedAfter gptkb:W._Hugh_Woodin
gptkbp:property strong large cardinal property
gptkbp:relatedTo measurable cardinal
strong cardinal
supercompact cardinal
gptkbp:symbol κ is Woodin
gptkbp:usedIn gptkb:descriptive_set_theory
inner model theory
determinacy
gptkbp:bfsParent gptkb:Ramsey_cardinal
gptkb:Large_cardinal_hypotheses
gptkbp:bfsLayer 6