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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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Strictly increases with stronger axioms
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gptkbp:example
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gptkb:Mahlo_cardinal_axiom
gptkb:Ramsey_cardinal_axiom
gptkb:Woodin_cardinal_axiom
gptkb:Extendible_cardinal_axiom
gptkb:Huge_cardinal_axiom
gptkb:Inaccessible_cardinal_axiom
gptkb:Indescribable_cardinal_axiom
gptkb:Measurable_cardinal_axiom
gptkb:Reinhardt_cardinal_axiom
gptkb:Strong_cardinal_axiom
gptkb:Supercompact_cardinal_axiom
gptkb:Weakly_compact_cardinal_axiom
0# exists
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gptkbp:field
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gptkb:Set_theory
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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:influencedBy
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gptkb:Kurt_Gödel
gptkb:Paul_Cohen
gptkb:W._Hugh_Woodin
gptkb:Ronald_Jensen
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gptkbp:motive
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Study the hierarchy of infinite sets
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gptkbp:notableFigure
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gptkb:Jean-Pierre_Serre
gptkb:Kurt_Gödel
gptkb:Paul_Cohen
gptkb:Solomon_Feferman
gptkb:William_Mitchell
gptkb:Andrés_Caicedo
gptkb:Donald_A._Martin
gptkb:John_Steel
gptkb:W._Hugh_Woodin
gptkb:Richard_Laver
gptkb:Matthew_Foreman
gptkb:Kenneth_Kunen
gptkb:Akihiro_Kanamori
gptkb:Józef_Tarski
gptkb:Jindřich_Zapletal
gptkb:Peter_Koellner
gptkb:Menachem_Magidor
gptkb:Ronald_Jensen
gptkb:Sy-David_Friedman
Hugh Woodin
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gptkbp:purpose
|
Postulate the existence of large cardinals
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gptkbp:relatedTo
|
gptkb:Continuum_hypothesis
gptkb:Zermelo–Fraenkel_set_theory
gptkb:Axiom_of_choice
gptkb:Determinacy_axioms
gptkb:Inner_model_theory
Descriptive set theory
Forcing
Large cardinal
Hierarchy of consistency strength
Reflection principles
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gptkbp:status
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Independent of ZFC
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gptkbp:studiedBy
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20th century
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gptkbp:usedIn
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gptkb:logic
gptkb:Foundations_of_mathematics
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gptkbp:bfsParent
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gptkb:The_foundations_of_mathematics
gptkb:Axiom_of_Constructibility
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gptkbp:bfsLayer
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7
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