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gptkbp:instanceOf
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gptkb:Titan
set theory concept
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gptkbp:consistencyStrength
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higher than ZFC
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gptkbp:example
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gptkb:Erdős_cardinal_axiom
gptkb:Mahlo_cardinal_axiom
gptkb:Ramsey_cardinal_axiom
gptkb:Vopěnka_cardinal_axiom
gptkb:Woodin_cardinal_axiom
gptkb:extendible_cardinal_axiom
gptkb:huge_cardinal_axiom
gptkb:inaccessible_cardinal_axiom
gptkb:indescribable_cardinal_axiom
gptkb:ineffable_cardinal_axiom
gptkb:measurable_cardinal_axiom
gptkb:strongly_compact_cardinal_axiom
gptkb:subtle_cardinal_axiom
gptkb:supercompact_cardinal_axiom
gptkb:weakly_compact_cardinal_axiom
0# exists
strong cardinal axiom
superstrong cardinal axiom
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gptkbp:field
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gptkb:mathematics
gptkb:set_theory
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gptkbp:firstAppearance
|
20th century
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https://www.w3.org/2000/01/rdf-schema#label
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large cardinal axioms
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gptkbp:implies
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the existence of infinite cardinals with strong properties
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gptkbp:motive
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explore the hierarchy of infinite cardinalities
analyze the structure of the set-theoretic universe
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gptkbp:namedFor
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set theorists
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gptkbp:purpose
|
postulate the existence of large cardinals
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gptkbp:relatedTo
|
gptkb:continuum_hypothesis
gptkb:Gödel's_constructible_universe
axiom of choice
forcing
large cardinal
consistency strength hierarchy
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|
gptkbp:status
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consistent with ZFC (if ZFC is consistent)
not provable in ZFC
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gptkbp:usedIn
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gptkb:descriptive_set_theory
independence proofs
inner model theory
determinacy results
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gptkbp:bfsParent
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gptkb:Zermelo-Fraenkel_set_theory
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gptkbp:bfsLayer
|
5
|