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gptkbp:instanceOf
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gptkb:set_theory
|
|
gptkbp:abbreviation
|
gptkb:ZF
|
|
gptkbp:alternativeTo
|
gptkb:Naive_set_theory
|
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gptkbp:basisFor
|
gptkb:ZFC_set_theory
most formalizations of mathematics
|
|
gptkbp:category
|
gptkb:logic
gptkb:mathematics
gptkb:set_theory
|
|
gptkbp:consistency
|
undecidable within ZF
|
|
gptkbp:excludes
|
gptkb:Axiom_of_Choice
|
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gptkbp:extendsTo
|
gptkb:ZFC_set_theory
|
|
gptkbp:field
|
gptkb:logic
gptkb:set_theory
|
|
gptkbp:formedBy
|
1908
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|
gptkbp:fullName
|
gptkb:Zermelo–Fraenkel_set_theory
|
|
gptkbp:hasAxiom
|
gptkb:Axiom_of_Empty_Set
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
gptkb:Axiom_of_Foundation
|
|
gptkbp:hasModel
|
gptkb:constructible_universe
cumulative hierarchy
|
|
gptkbp:hasSubgroup
|
gptkb:ZFC_set_theory
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
ZF set theory
|
|
gptkbp:influencedBy
|
gptkb:Russell's_paradox
|
|
gptkbp:isFoundationFor
|
most of modern mathematics
|
|
gptkbp:limitation
|
cannot prove its own consistency (Gödel's incompleteness theorems)
independence of axiom of choice
independence of continuum hypothesis
|
|
gptkbp:logicalFramework
|
gptkb:first-order_logic
|
|
gptkbp:namedAfter
|
gptkb:Ernst_Zermelo
gptkb:Abraham_Fraenkel
|
|
gptkbp:publishedIn
|
gptkb:Fraenkel,_1922
gptkb:Zermelo,_1908
|
|
gptkbp:purpose
|
provide a rigorous foundation for mathematics
|
|
gptkbp:usedIn
|
gptkb:category_theory
foundations of mathematics
model theory
proof theory
|
|
gptkbp:相关理论
|
gptkb:Morse–Kelley_set_theory
gptkb:Tarski–Grothendieck_set_theory
gptkb:Von_Neumann–Bernays–Gödel_set_theory
|
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gptkbp:bfsParent
|
gptkb:ZFC_set_theory
|
|
gptkbp:bfsLayer
|
7
|