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gptkbp:instanceOf
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gptkb:set_theory
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gptkbp:abbreviation
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gptkb:ZFC
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gptkbp:basisFor
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most mathematical objects
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gptkbp:formedBy
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early 20th century
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gptkbp:fullName
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gptkb:Zermelo–Fraenkel_set_theory_with_the_axiom_of_choice
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gptkbp:generalizes
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gptkb:Zermelo_set_theory
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gptkbp:hasAxiom
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gptkb:Axiom_of_Choice
gptkb:Axiom_of_Extensionality
gptkb:Axiom_of_Infinity
gptkb:Axiom_of_Pairing
gptkb:Axiom_of_Power_Set
gptkb:Axiom_of_Regularity
gptkb:Axiom_of_Union
gptkb:Axiom_Schema_of_Replacement
gptkb:Axiom_Schema_of_Separation
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gptkbp:hasModelIf
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ZFC is consistent
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gptkbp:hasSubgroup
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gptkb:ZFC+large_cardinal_axioms
class of all set theories
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https://www.w3.org/2000/01/rdf-schema#label
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ZFC set theory
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gptkbp:isComparedTo
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gptkb:Morse–Kelley_set_theory
gptkb:Kripke–Platek_set_theory
gptkb:New_Foundations
gptkb:Von_Neumann–Bernays–Gödel_set_theory
gptkb:Zermelo_set_theory
gptkb:ZF_set_theory
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gptkbp:isConsistentIf
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no contradiction can be derived from its axioms
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gptkbp:isCountable
|
in some models
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gptkbp:isFormalizedIn
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gptkb:first-order_logic
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gptkbp:isFoundationFor
|
modern mathematics
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gptkbp:isIncomplete
|
by Gödel's incompleteness theorems
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gptkbp:isIndependentOf
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gptkb:Axiom_of_Choice
gptkb:Continuum_Hypothesis
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gptkbp:isUncountable
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in other models
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gptkbp:isUndecidable
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in first-order logic
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gptkbp:namedAfter
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gptkb:Ernst_Zermelo
gptkb:Thoralf_Skolem
gptkb:Abraham_Fraenkel
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gptkbp:referencedIn
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gptkb:Gödel's_incompleteness_theorems
gptkb:axiom_of_determinacy
gptkb:constructible_universe
gptkb:descriptive_set_theory
gptkb:Cohen's_forcing
gptkb:large_cardinal_hypotheses
model theory
independence proofs
inner model theory
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gptkbp:usedBy
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most mathematicians
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gptkbp:usedIn
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gptkb:logic
gptkb:set_theory
foundations of mathematics
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gptkbp:bfsParent
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gptkb:Axiom_of_Separation
gptkb:MK_set_theory
gptkb:Axiom_of_pairing
gptkb:community_library_(mathlib)
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gptkbp:bfsLayer
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6
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