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gptkbp:instanceOf
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gptkb:set_theory
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gptkbp:abbreviation
|
gptkb:Zermelo–Fraenkel_set_theory_with_the_axiom_of_choice
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gptkbp:basisFor
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gptkb:cardinal_arithmetic
ordinal arithmetic
formalization of mathematics
theory of infinite sets
|
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gptkbp:developedBy
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gptkb:Ernst_Zermelo
gptkb:Thoralf_Skolem
gptkb:Abraham_Fraenkel
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gptkbp:formedBy
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early 20th century
|
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gptkbp:fullName
|
gptkb:Zermelo–Fraenkel_set_theory_with_the_axiom_of_choice
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gptkbp:hasAxiom
|
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_Replacement
gptkb:Axiom_of_Separation
gptkb:Axiom_of_Union
|
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gptkbp:hasModel
|
gptkb:constructible_universe
|
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gptkbp:hasSubgroup
|
gptkb:first-order_logic
|
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https://www.w3.org/2000/01/rdf-schema#label
|
ZFC
|
|
gptkbp:isAxiomatizedBy
|
gptkb:first-order_logic_with_equality
nine axioms
|
|
gptkbp:isComparedWith
|
gptkb:Kripke–Platek_set_theory
gptkb:New_Foundations
gptkb:Von_Neumann–Bernays–Gödel_set_theory
|
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gptkbp:isConsistentRelativeTo
|
no known contradiction
|
|
gptkbp:isFoundationFor
|
most of modern mathematics
|
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gptkbp:isIndependentOf
|
gptkb:Axiom_of_Choice
gptkb:Continuum_Hypothesis
|
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gptkbp:relatedTo
|
gptkb:Gödel's_incompleteness_theorems
gptkb:Peano_arithmetic
gptkb:category_theory
gptkb:axiom_of_determinacy
gptkb:axiom_schema_of_replacement
gptkb:axiom_schema_of_specification
gptkb:constructible_universe
gptkb:large_cardinal_axioms
gptkb:second-order_logic
model theory
forcing
|
|
gptkbp:usedBy
|
gptkb:mathematician
logicians
philosophers of mathematics
|
|
gptkbp:usedIn
|
gptkb:logic
gptkb:set_theory
foundations of mathematics
|
|
gptkbp:bfsParent
|
gptkb:Continuum_hypothesis
gptkb:Axiom_of_Extensionality
gptkb:Axiom_of_Replacement
gptkb:Zermelo-Fraenkel_set_theory
gptkb:Set_Theory
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gptkbp:bfsLayer
|
5
|