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gptkbp:instanceOf
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gptkb:Titan
gptkb:set_theory_concept
|
|
gptkbp:consistencyStrength
|
higher than ZFC
|
|
gptkbp:example
|
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
|
|
gptkbp:field
|
gptkb:mathematics
gptkb:set_theory
|
|
gptkbp:firstAppearance
|
20th century
|
|
gptkbp:implies
|
the existence of infinite cardinals with strong properties
|
|
gptkbp:motive
|
explore the hierarchy of infinite cardinalities
analyze the structure of the set-theoretic universe
|
|
gptkbp:namedFor
|
set theorists
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|
gptkbp:purpose
|
postulate the existence of large cardinals
|
|
gptkbp:relatedTo
|
gptkb:continuum_hypothesis
gptkb:Gödel's_constructible_universe
gptkb:large_cardinal
axiom of choice
forcing
consistency strength hierarchy
|
|
gptkbp:status
|
consistent with ZFC (if ZFC is consistent)
not provable in ZFC
|
|
gptkbp:usedIn
|
gptkb:descriptive_set_theory
independence proofs
inner model theory
determinacy results
|
|
gptkbp:bfsParent
|
gptkb:ZFC
gptkb:Zermelo-Fraenkel_set_theory_with_the_axiom_of_choice_(ZFC)
gptkb:Zermelo-Fraenkel_set_theory
|
|
gptkbp:bfsLayer
|
6
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
large cardinal axioms
|