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A cardinal satisfying one of several strong closure, compactness, measure, or elementary-embedding properties used to calibrate set-theoretic strength.
ZFC does not prove that inaccessible, measurable, or supercompact cardinals exist, assuming the usual consistency hypotheses; their existence is adopted through additional axioms.
wp-large-cardinalnlab-large-cardinalsep-large-cardinalsEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Select cardinals satisfying additional closure, compactness, measure, or elementary-embedding properties.
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
wp-large-cardinalsep-large-cardinalsEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Strongly inaccessible cardinals form an early benchmark in the large-cardinal hierarchy.
The target is a member or subtype of the broader source class.
wp-inaccessible-cardinalsep-large-cardinalsThis is an authored directed relation from the source endpoint to the target endpoint.
Measurable cardinals are a stronger large-cardinal notion defined by a highly complete nonprincipal measure.
The target is a member or subtype of the broader source class.
wp-measurable-cardinalsep-large-cardinalsThis is an authored directed relation from the source endpoint to the target endpoint.
Supercompact cardinals satisfy compactness properties at every greater scale.
The target is a member or subtype of the broader source class.
wp-supercompact-cardinalsep-large-cardinals